Manajemen | Fakultas Ekonomi Universitas Maritim Raja Ali Haji 073500103288619034
Journal of Business & Economic Statistics
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Martingale Property of Exchange Rates and
Central Bank Interventions
Kamil Yilmaz
To cite this article: Kamil Yilmaz (2003) Martingale Property of Exchange Rates and
Central Bank Interventions, Journal of Business & Economic Statistics, 21:3, 383-395, DOI:
10.1198/073500103288619034
To link to this article: http://dx.doi.org/10.1198/073500103288619034
View supplementary material
Published online: 01 Jan 2012.
Submit your article to this journal
Article views: 57
View related articles
Citing articles: 4 View citing articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ubes20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 13 January 2016, At: 01:03
Martingale Property of Exchange Rates
and Central Bank Interventions
Kamil Y ILMAZ
College of Administrative Sciences and Economics, Koç University, Rumelifeneri Yolu,
Sariyer 34450, Istanbul, Turkey (kyilmaz@ku.edu.tr )
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
This article uses the variance ratio-based multiple comparison test and the Richardson–Smith Wald test
procedures to test for the martingale property of daily exchange rates of seven major currencies vis-à-vis
the U.S. dollar. To allow for the possibility that exchange rates are not governed by a single process
throughout the oat, the test statistics are calculated and plotted for xed-length moving subsample windows rather than being applied to the full sample. The results show that exchange rates do not always
follow the martingale process. During the times of coordinated central bank interventions, exchange rates
deviate from the martingale property.
KEY WORDS: Fixed-length moving subsample window; Joint variance ratio test; Multiple comparison
test; Richardson–Smith Wald test.
1.
INTRODUCTION
Since the breakdown of the Bretton Woods system in the
early 1970s, exchange rate economics has become an area of
active research for economists. Earlier, the focus was more on
structural models to explain exchange rate behavior over time.
However, since Meese and Rogoff (1983) showed that the structural models had inferior performance than a naïve martingale
in out-of-sample forecasts, many studies strived to uncover the
empirical regularities in exchange rate behavior.
Baillie and Bollerslev (1989) found evidence supporting the
presence of cointegration among 7 major daily exchange rates
during the period between 1980 and 1986. However, Diebold,
Gardeazabal, and Yõlmaz (1994) showed that the results obtained by Baillie and Bollerslev (1989) were sensitive to the
inclusion of a drift in the tests, which happened to be in the
data during the 1980–1986 period. Once the drift is included,
evidence turns against the cointegration, and the random walk
performs better than alternative models in out-of-sample forecasts.
Applying the variance ratio (VR) test to weekly exchange
rates between August 1974 and March 1989, Liu and He
(1991) rejected the martingale hypothesis for the German mark
(DEM), Japanese yen (JPY), and British pound (GBP), but
failed to do so for the Canadian dollar (CD$) and French franc
(FRF) vis-à-vis the U.S. dollar (US$). In a recent follow-up,
Fong, Koh, and Ouliaris (1997) emphasized the shortcomings
of Liu and He’s analysis. They studied the statistical performance of two different multiple VR tests of the martingale hypothesis: Hochberg’s (1974) multiple comparison test (MCT)
and Richardson and Smith’s (1991) (RS) Wald test. Then they
applied these tests to exchange rates over the October 1979–
March 1989 period. They found that the RS test failed to reject
the martingale hypothesis for all ve exchange rates considered, whereas the MCT continued to reject the hypothesis for
the FRF, DEM, and JPY.
Tests of the martingale hypothesis are related to the correlogram of log exchange rate increments. They evaluate whether
the autocorrelation coefcients at different lags and leads
equal 0. Liu and He (1991) and Fong et al. (1997), among others, conducted tests of martingale property in nancial time
series for a given time period and reached a verdict about the
behavior of the asset prices during that period. However, it is not
correct to assume that the process that governs the time series
behavior of exchange rates stayed unchanged during a 25-year
period. Central bank interventionsin the foreign exchange (FX)
markets or the frequent realignments in the exchange rate mechanism of the European monetary system (EMS) are some factors that might possibly have affected the behavior of exchange
rates over time. For example, Dominquez (2001) provided evidence that central bank interventions inuence intradaily FX
returns and volatility.
Given the fact that central banks of major industrial countries
have changed their stance with respect to market intervention
over time, there is a possibility that policy shifts can result in
a change in the time series behavior of exchange rates. For example, as Dominquez (1998) stated; after 4 years of passive
intervention policy between 1981 and 1984, the Federal Reserve became more active toward the end of 1985 to slow down
the appreciation of the dollar against other major currencies.
These shifts in the policy stance must be taken into account.
One alternative then is to assume a priori that there is a structural break in the data. For example, taking into account the
changes in the Federal Reserve’s operating procedures, Liu and
He (1991) treated October 1979 as a structural breakpoint and
divided their sample in two. This is a step in the right direction,
but it still falls short of a satisfactory solution for the problem at
hand. Even if a change occurs in the time series behavior of exchange rates, this does not have to be a signicant discrete jump
in the underlying parameters. As long as the change takes the
form of a slow, continous process or a small jump in the parameters, structural break tests are unlikely to capture the change
(Diebold and Chen 1996).
In this article it is suggested that tests of the martingale property in exchange rates need to control for the sensitivity of the
results to the particular sample period used. For that reason,
tests of the martingale property were conducted in movingsubsample windows with a xed length of 1,000 daily observations. The test statistics for all subsample windows are plotted. Plotting the test statistics for subsample windows facilitates
383
© 2003 American Statistical Association
Journal of Business & Economic Statistics
July 2003, Vol. 21, No. 3
DOI 10.1198/073500103288619034
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
384
Journal of Business & Economic Statistics, July 2003
observation of whether there is any change in the behavior of
exchange rates over time.
Following Fong et al. (1997), the present work uses two joint
VR test procedures. These are the MCT proposed by Chow and
Denning (1993) and the joint VR test developed by Richardson and Smith (1991). These tests are applied to changes of
daily New York spot exchange rates of the U.S. dollar vis-à-vis
seven major currencies: the DEM, JPY, GBP, FRF, Swiss franc
(CHF), CD$, and Italian lira (ITL). The sample period starts on
January 1, 1974 and ends on February 12, 2001.
This article is not an attempt to develop a theory that shows
how the martingale property can be rejected after the central
bank interventions. However, theoretical models can be used
to establish the link between the monetary policy actions and
the violation of the martingale. McCallum (1994) and Meredith and Chinn (1998) presented theoretical models showing that
the violation of the uncovered interest parity (UIP) can be due
to the presence of feedback mechanisms between the exchange
rates, ination, output, and interest rates. Under the assumption
that the daily risk-free interest rate is 0, which is not a totally
unjustied approximation with daily data, the UIP implies that
the daily exchange rate is a martingale. Based on this assumption, it is theoretically possible for the monetary policy feedback mechanisms to cause daily exchange rates to deviate from
martingale behavior.
The article is organized as follows. Section 2 briey reviews
the developments in the foreign exchange markets since the
oat, as well as the literature on exchange rate behavior. Section 3 provides a detailed account of the joint VR tests used in
the analysis, and Section 4 presents the empirical results. Section 5 concludes by summarizing the results.
2.
EXCHANGE RATES UNDER THE FLOAT:
THE MARKET, CENTRAL BANK
INTERVENTIONS, AND THE LITERATURE
2.1
Foreign Exchange Markets
Established as an informal market in the 1960s, FX markets
grew rapidly in the 1980s and especially in the 1990s. Accord-
ing to surveys conducted by the Bank for International Settlements (BIS) every 3 years, since April 1989 average daily
turnover in foreign exchange markets worldwide (adjusted for
cross-border and local double-counting and evaluated at April
1998 exchange rates) increased by 33%, 29%, and 46% between consecutive triennial surveys.
The U.S. dollar has been the dominant currency in both the
spot and the forward and swap transactions. Its share in daily
turnover has uctuated between 80% and 90% (when reported
on one side of the transactions). The sum of the remaining six
major currencies (all included in our analysis) accounts for a
market share approximately equal to that of the U.S. dollar. The
remaining 20%–30% of the total (200%) market turnover has
been accounted by other currencies from Europe and as well as
from other parts of the world (Table 1).
BIS surveys also include information on the liquidity of bilateral FX transactions. U.S. dollar bilateral exchange rates against
six major currencies in the sample herein form the most liquid
segments of the FX market. For example, 63% of average daily
trade volume in April 1998 was accounted by the bilateral U.S.
dollar transactions against other major currencies included in
our analysis, except ITL.
The data used in this article are reported noon spot exchange
rates in New York. For that reason, it is quite relevant to study
the turnover of each currency in the New York market. Table 1
reports the average daily turnover in 1995 for the seven major
currencies in the New York market in their respective base markets and the world market as a whole.
Based on this data, the currencies can be classied into three
groups. With $104 and $55 billion daily turnovers, the DEM
and JPY are the two most actively traded currencies in the
New York market after the US$. Next are the three European
currencies (the GBP, FRF, and CHF), each with an approximate $20 billion daily turnover. Finally, the daily turnovers for
the CD$ and Australian dollar (AU$) are less than $10 billion.
Table 1 reveals that spot markets went through a rapid expansion in the rst half of the 1990s. Whereas on average only
$140 billion worth of currency changed hands daily in 1992,
according to BIS surveys this amount increased to more than
Table 1. Total Daily Turnover in FX Markets
April 1992
US$/DEM
US$/JPY
US$/GBP
US$/CHF
US$/CD$
DEM/GBP
US$/FRF
DEM/JPY
US$/AU$
DEM/CHF
Other
Total
April 1995
Total
(bil $)
Share in
total (%)
Of which
spot (%)
192:2
154:8
76:5
48:8
25:4
23:3
18:6
18:2
17:9
13:3
195:9
784:9
24
20
10
6
3
3
2
2
2
2
25
30
16
9
6
2
5
1
4
1
3
23
Total
(bil $)
US$/DEM
253:9
US$/JPY
242
US$/othEMS
104:3
US$/GBP
77:6
US$/CHF
60:5
US$/FRF
60
DEM/othEMS
38:2
US$/CD$
38:2
DEM/FRF
34:4
US$/AU$
28:7
DEM/JPY
24
DEM/GBP
21:3
DEM/CHF
18:4
Other
135:4
Total
1136:9
April 1998
Share in
total (%)
Of which
spot (%)
22
21
9
7
5
5
3
3
3
3
2
2
2
12
56
36
33
37
17
32
86
31
79
86
Total
(bil $)
US$/DEM
290:5
US$/JPY
266:6
US$/othEMS
175:8
US$/GBP
117:7
US$/CHF
78:6
US$/FRF
57:9
US$/CD$
50
US$/AU$
42:2
DEM/othEMS
35:1
DEM/GBP
30:7
DEM/JPY
24:2
DEM/CHF
18:4
US$/XEU
16:6
Other
237:2
Total
1441:5
Share in
total (%)
20
18
12
8
5
4
3
3
2
2
2
1
1
16
Of which
spot (%)
49
45
14
33
30
16
25
33
75
79
77
NOTE: After adjusting for double counting in interbank transactions, the average daily turnover in the New York market was 26.1 billion per day in April 1983. Other currencies in the EMS are
denoted by othEMS.
Source: Bank of International Settlements (1992, 1995, 1998).
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
$500 billion in 1995. The expansion of the spot FX markets
continued in the second half of the 1990s, although with some
slowdown. Whereas total daily FX market turnover increased
by 27% from 1995 to 1998, most of this increase was due to the
expansion in the forward FX markets. Daily total spot market
turnover increased by only 14%, to $590 billion.
Comparable gures for the 1970s and 1980s are not available. However, it is evident from the available data that the FX
markets have gone through a period of rapid expansion in the
1990s.
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
2.2
Central Bank Interventions
Especially in the earlier years of the oat, FX markets have
gone through periods of instability. All major industrial countries were affected adversely by oil crises in 1973 and 1979.
The oil price hikes not only disturbed their external balances,
but also led to high ination rates never before seen in these
countries in the postwar period. The impact on the relative values of major currencies was unprecedented, leading to subtantial volatility in the foreign exchange markets. Due to increased
inationary pressures and rapid decline in the political power of
the Carter administration, toward the end of the 1970s, the U.S.
dollar started to lose value against other major currencies.
In the rst 2 years of the oat central banks intervened sporadically with no coordination. The intervention was seen as a
necessary policy tool to stabilize highly volatile FX markets.
However, in October 1974 the U.S. Federal Reserve, the German Bundesbank, and the Swiss National Bank began intervening in a concerted fashion to control the volatility of the DEM
and CHF exchange rates (Schwartz 2000). The coordinated interventions continued throughout the 1970s, with the participation of the Bank of Japan after September 1977. But despite the
U.S. interventions, the U.S. dollar continued to depreciate until
1980.
Differences among industrial countries’ responses to oil price
shocks continued to shape the policy issues and debates in the
1980s. To bring ination under control, the Federal Reserve began to follow a tight monetary policy in 1980. The resulting
high interest rates attracted capital inows to the United States,
leading to the appreciation of the U.S. dollar. The appreciation
of the dollar lasted until 1985, and at its peak in late February and early March 1985, the dollar was overvalued by 40%
(Obstfeld 1990).
After coming to power in 1981, the Reagan administration
followed a policy of little intervention. It refused any coordinated intervention in FX markets except in an emergency case.
The concerted interventions that occurred for a short period
in June–August 1982 were consistent with this policy stance.
However, faced with ever rising dollar for over 4 years, the U.S.
government could not stick to its promise and had to search for
coordination among major central banks.
The period 1986–1991 was a time of concerted interventions
in FX markets around the world. In September 1985, G-7 nance ministers agreed to intervene in the worldwide FX markets in a concerted fashion when they nd it necessary. This
agreement, known as the Plaza Accord, marked a drastic change
in the policy stance of the major central banks in terms of the
movements of exchange rates. Soon after the signing of the
385
Plaza Accord came a heavy bout of concerted interventions.
Most of the interventions took the form of selling U.S. dollars
against other major currencies, especially against the DEM and
the JPY.
These interventions paid off; the US$ started to lose much
of the value that it had gained against other currencies, thanks
in large part to the massive sterilized interventions by the Federal Reserve, the Bundesbank, and the Bank of Japan. These interventions were effective in signaling the policy stance of the
monetary authorities and thus could lead to some predictable
changes in the exchange rates during the second half of 1980s
(Dominquez 1990).
After the success of the Plaza Accord, leading central
bankers continued to work closely to prevent wide swings in
the exchange rates. The Louvre Accord of February 1987 was
an explicit step in this direction. It set unannounced and secret
target bands for the DEM/US$ (between 1.6 and 1.9) and the
JPY/US$ (between 120 and 140) exchange rates, beyond which
central banks had agreed to intervene.
According to Catte, Galli, and Rebecchini (1994), the leading central banks had undertaken 17 concerted interventions
between 1985 and 1991. The U.S. Federal Reserve, the Bundesbank, and the Bank of Japan were the major players in
every intervention. During this period, none of the G-3 central
banks undertook any intervention contradicting the policies of
the other two. McKinnon (1996, pp. 67–68) emphasized that 16
out of 17 interventions during this period could be desribed as
“leaning against the wind.”
Contrary to the implications of the theory, there is consensus among economists on whether central bank interventions
have some lasting effects on FX markets. In the absence of
an explicit coordination, these interventions had to be sterilized to keep the monetary stability intact. Baillie and Osterberg
(1997) showed that in the 1980s, the effects of sterilized interventions lasted beyond the day of intervention. Dominquez
(1990) showed that the effects of sterilized intervention diminish monotonically over time, and that concerted interventions
are more effective than individual interventions in generating
the desired exchange rate behavior.
McKinnon (1993) claimed that these infrequently exercised,
explicitly announced concerted interventions affected the FX
markets, simply because they signaled the policy stance of the
major central banks and, thus inuenced the expectations about
the future behavior of exchange rates. Obstfeld (1990), on the
other hand, claimed the contrary. Based on anecdotal evidence,
he argued that sterilized interventions were effective only when
backed by appropriate monetary policy adjustments. Together,
these studies show that changes in FX monetary, or scal policies do have some lasting impact on FX markets.
In addition to these studies, Dominquez (1998) showed that
central bank interventions on average led to higher volatility in
bilateral DEM/US$ and JPY/US$ exchange rates. With a value
of 6.14, the maximum conditional volatility for DEM/US$ occurred in November 2, 1978, soon after the Carter administration’s decision to intervene in markets to support a declining
U.S. dollar. In the case of the JPY/US$ exchange rate, the maximum volatility was 3.27, observed just 2 days after the Plaza
Accord was signed.
Because not all of the central banks were involved in all of
the concerted policy interventions, market interventions cannot
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
386
Journal of Business & Economic Statistics, July 2003
be expected to affect bilateral exchange rates of the U.S. dollar
vis-à-vis all other major currencies. Being the issuers of most
traded currencies, the Federal Reserve, the Bundesbank,and the
Bank of Japan intervened selectively to affect the value of the
US$ vis-à-vis the DEM, JPY, and, to some extent, GBP. Consequently, if policy interventions do have lasting impact, then
these bilateral exchange rates are relatively more likely to diverge from martingale behavior during the period of concerted
policy interventions.
In comparison to the 1980s, throughout the 1990s fewer FX
market interventions occurred. According to news reports, interventions of the 1990s are in general smaller in magnitude
than those of the previous decade. Nine relatively small-scale
interventions were undertaken between 1991 and 1999 (Table 2). One important reason behind this change was the relative calm in the FX markets around the world in the 1990s. The
large swings that characterized the FX markets in the 1980s,
especially when the U.S. dollar was concerned, were not observed in the 1990s; therefore, the need for policy intervention
occurred less frequently and at a smaller scale.
The only exception to the relative calm of the 1990s was the
ERM crisis of September 1992. After excessive speculative attacks, the GBP, ITL, and the Swedish kroner dropped out of
the ERM and were allowed to oat freely since then. During
the ERM crisis, central banks of the respective countries intervened heavily to defend their ERM exchange rates. The nancial crises in Mexico, East Asia, and Russia did not have
any major impact in the worldwide FX markets for major currencies and thus did not necessitate policy intervention by the
central banks of the G-7 countries. Recently, calls for concerted
intervention intensied after the apparent failure of the Euro to
recover its losses against the U.S. dollar after the Euro’s inauguration in January 1999.
2.3
Literature on the Martingale Property
of Exchange Rates
Since the breakdown of the Bretton Woods system, numerous
studies on the behavior of exchange rates under the oat have
been reported. The work of Meese and Rogoff (1983) has been
among the most inuential. Using short-horizon log exchange
rate changes, these authors showed that the structural models
of exchange rate determination (i.e., the exible-price monetary model, the sticky-price monetary model, and the portfoliobalance model) do not perform better than the random-walk
model in out-of-sample forecasts.
Using more recently developedcointegrationtest procedures,
Baillie and Bollerslev (1989) found evidence supporting the
presence of cointegration among seven major daily exchange
rates during the period 1980–1986. A nding of cointegration
would mean a long-run equilibrium relationship between exchange rates. Short-run deviations from this long-run equilibrium relationship (called the error-correction model) can be predicted. Using a maximum likelihood–based Johansen test procedure, Diebold et al. (1994) showed that the results obtained
by Baillie and Bollerslev (1989) were sensitive to the inclusion of a drift in the tests, which happened to be in the data
during the 1980–1986 period. Once the drift is included, evidence turns against the cointegration. Diebold et al. (1994) also
showed that the random walk performs better in out-of-sample
forecasts compared with alternatives such as error-correction
model that would be implied by the presence of cointegration
and unrestricted vector autoregression (VAR).
Besides the studies focusing on short-horizon log exchange
rate changes, a whole set of studies provides direct and indirect evidence against random-walk behavior at long horizons.
First, a series of panel studies show that purchasing power parity, an alternative to random-walk behavior, holds in the long
run but not in the short run (Lothian 1996, Papell 1997). Second, using long-horizon changes, Lothian and Taylor (1996)
showed that the real exchange rate mean reverts and that univariate rst-order autoregressive models perform better than alternative random-walk models both before and after the oat.
Third, Mark (1995), Chinn and Meese (1995), and Mark and
Sul (2001) found that exchange rate deviations from monetary
fundamentals predict future exchange rates. Finally, Meredith
and Chinn (1998) showed that uncovered interest parity may
hold over long horizons, but not over short horizons.
Without a doubt, these results provide evidence that at long
horizons, exchange rates do not follow random-walk behavior.
Placed against the evidence supporting random-walk behavior
at short horizons, this result raises a serious question: Because
the long-horizon log exchange rate change is the sum of shorthorizon changes, it is surprising that there is little evidence
against the random walk over short horizons. In this regard, this
article should be viewed as an attempt to reconcile results of the
short-horizon tests with those of the long-horizon tests.
Attempts have been made to use semiparametric procedures
to test for the martingale property of exchange rates. The main
problem with these tests arises if the null hypothesis is rejected,
in which case there is no way to determine the alternative hypothesis. Liu and He (1991) applied the VR test for the martingale property on ve major exchange rates (DEM, JPY, GBP,
CD$, and FRF) against the US$ over the sample period August
1974–March 1989. They used the VR test and rejected the martingale property for the DEM, JPY, and GBP, but failed to do
so for the CD$ and FRF vis-à-vis the US$ for weekly exchange
rates.
Fong et al. (1997) studied the statistical performance of
two different multiple VR tests of the martingale hypothesis:
Hochberg’s MCT and the RS Wald test. Fong et al. (1997) took
their analysis one step further and applied the multiple VR test
and the RS Wald test to the same data. They started by showing that in small samples, the RS Wald test had better power
properties than the multiple VR test. When they applied both
tests to the October 1979–March 1989 period, the RS Wald test
failed to reject the martingale hypothesis, whereas the multiple
VR test continued to reject the hypothesis for the FRF, DEM,
and JPY.
All studies testing the martingale property of exchange rates
were based on a xed sample period. This sample period is dictated either by the availability of the data or by visible breaks,
such as a switch in the monetary or exchange rate policy in
the country of interest. For example, Liu and He (1991) divided their sample into 1974–1978 and 1979–1989 to take
into account a major change in U.S. monetary policy. In their
analysis of the implications of the European ERM on the exchange rate dynamics, Anthony and MacDonald (1998) divided
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
387
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Table 2. Chronology of Events Concerning the FX Markets
Date
Event
October 1978
Feb–Apr 1979
March 1979
Sep 23, 1979
Nov 30, 1979
Nov 1979–Jan 1980
Feb–Apr 1980
Mar 02, 1980
Mar 17, 1980
FED bought US$.
Central banks’ total intervention in this period amounted to $38 bil.
Inception of the ERM.
ERM realignment (ERM re): FRF devalued.
ERM re: ITL devalued.
Central banks’ total intervention in this period amounted to $24 bil.
Central banks’ total intervention in this period amounted to $37 bil.
Bank of Japan’s (BoJ) 5-point plan to support yen.
Coordinated Intervention (CI): BoJ, Bundesbank (BuBa) and
Swiss National Bank (SNB) sold $300 mil.
ERM re: ITL devalued by 6%.
FED bought $500 mil.
No-intervention policy announced by the Reagan administration.
French Central bank intervened.
No intervention by the FED in this period.
BoJ sold $1 bil.
Bundesbank sold $12.8 mil.
Canada Central bank sold US$.
Swiss and four other Central banks sold $100 mil.
ERM re: FRF and ITL down by 3%, DEM and NLG up by 5.5%.
French Central bank hiked interest rates to protect franc.
ERM re: FRF, ITL fall in value; DEM, NLG up.
FED intervened.
Canada Central bank: bought C$1.6 bil.
FED intervened.
CI: DEU, JPN, CHE, NLD, GBR Central Banks sold $1 bil.
FED intervened.
FED intervened.
ERM re: Down: FRF (2.5%), ITL (2.5%), Irish Punt, IRP (3.5%);
Up: DEM (5.5%), NLG (3.5%), DNK (2.5%), BFR and LFR (1.5%).
CI: Central banks sold 2.5–3 bil.
Bank of Canada raised interest rates to protect the value of Canadian dollar.
Bundesbank sold US$.
CI: sold $1–2 bil.
Ohio bank crisis.
ERM re: ITL devalued.
Plaza Accord: Central banks sold $7 bil (between Sep22–Oct31).
Bank of Canada sold US$850 mil.
BoJ: mild intervention.
ERM re: FRF down by 3%, DEM and NLG up by 3%.
BEF, LFR and DNK up by 1%, ITL down.
ERM re: BFR, LFR fall in value; DEM, NLG up.
Louvre Accord: Central banks bought $3.5 bil between Mar 23–Apr 17.
CI: Central banks bought $4.06 bil.
FED bought $4.14 bil.
Interest rate cut by major European countries to stem the fall of the US$.
G-7 nance min reiterated their resolve to keep the US$ from falling further.
FED bought $818 mil.
FED mild int; BoJ inervened heavily to stop yen’s appreciation.
CI: Massive intervention.
CI: Central banks sold $2.93 bil.
CI: BoJ bought $1 bil; others $1 bil (FED sold JPY&DEM).
CI: Central banks sold US$.
CI: Central banks sold $10 bil.
CI: Central banks sold US$.
ERM re: ITL devalued against DEM.
CI: Central banks sold US$.
British pound joined the ERM.
CI: Central banks bought $1.5 bil.
CI: Central banks of DEU, CHE, DNK, BEL, ITA, and ESP sold US$.
US treasury announced it would act to reverse dollar appreciation.
ERM re: DNK, NLG devalued.
CI: 13 Central banks bought US$ against DEM.
Bank of England (BoE) bought GBP using 5% of its ofcial FX reserves.
BoE spent £15 bil equivalent of £44 bil FX reserves to keep
the GBP within its target band.
ERM Crisis: GBP, ITL and SWK left the EMS.
CI: FED and BoJ sold US$ to support JPY.
ERM re: Spanish Peseta and Portugese Escudo (6%) devalued.
ERM re: Irish Punt devalued.
ERM re: Spanish Peseta (8%) and Portugese Escudo (6.5%) devalued.
ERM bands expanded from 2.25% to 15%.
CI: 17 Central banks bought US$.
March 22, 1981
Mar 30, 1981
May 04, 1981
May 12, 1981
May–July 1981
July 23, 1981
Jul, 1981
Jul, 1981
August 4, 1981
Oct 4, 1981
March 25, 1982
June 12, 1982
June 14, 1982
May–June 1982
August 4, 1982
August 10, 1982
August 16, 1982
October 1982
March 21, 1983
July 29, 1983
March 15, 1984
June 25–28, 1984
Feb 27, 1985
Mar 18–20, 1985
June 20 1985
September 1985
Feb 11, 1986
Mar 18, 1986
April 6, 1986
Jan 12, 1987
Feb 21–22, 1987
Mar 22–Apr 10,1987
Nov 1987–Jan 1988
Dec 3, 1987
Dec 22, 1987
Feb–Apr 1988
Mar–Apr 1988
Apr 14–15, 1988
May–July 1988
Nov 17, 1988
Jan 11, 1989
May 22–Jun 7, 1989
Sep 24–Oct 5, 1989
Jan 8, 1990
Mar 5–7, 1990
October 1990
Feb 4–12, 1991
Mar 27, 1991
Jul 1, 1991
Apr 4, 1992
July 20–Aug 11 1992
Aug 26, 1992
Sep 14–16, 1992
Sep 17, 1992
Apr 22–27, 1993
Nov 22, 1992
Feb 1, 1993
May 13, 1993
Aug 2, 1993
May 4, 1994
(continued)
388
Journal of Business & Economic Statistics, July 2003
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Table 2. (continued)
Date
Event
Nov 2–3, 1994
Mar 2–3, 1995
Apr 5, 1995
Aug 15, 1995
Sep 22, 1995
Nov 26, 1996
Jul–Oct 1997
Jun 17, 1998
Aug 1998
Jan 12, 1999
FED bought $1.5 bil against JPY and DEM.
CI: FED, BoJ and BuBa bought $1.3 bil.
CI: FED, BoJ and BuBa bought $1 bil against JPY and DEM.
CI: FED, BoJ and BuBa bought $3 bil against JPY and DEM.
EU nance ministers’ meeting on EMU.
Italian lira rejoined the ERM.
Asian Crisis started.
CI: FED and BoJ sold $4 bil against JPY.
Russian Crisis.
BoJ bought $2–3 bil against JPY.
the 1979–1992 sample into subsamples using the date of currency’s realignment in the ERM as cutoff dates. Although this
allowed them to clean their data from the effects of the jumps in
the exchange rates during the realignment period, nevertheless
in some instances they were left with few data points (fewer
than 200 observations) to estimate VRs. However, both Lo and
MacKinlay (1988) and Richardson and Smith (1991) showed
that the VR-test has poor performance with small samples.
Moving xed-length subsample windows enables one to
identify shocks that signicantly alter the exchange rate behavior, such as the FX market interventions by central banks
and the ERM realignments in the case of European currencies.
These shocks on the exchange rate behavior are identied by
signicant jumps in the test statistic.
3.
JOINT VARIANCE RATIO TESTS
Tests of martingale hypothesis are related to the correlogram
of log exchange rate increments and evaluate whether the autocorrelation coefcients at different lags and leads are equal
to 0. Because tests of random walk do not run the risk of misspecication of the alternative hypothesis, they are expected to
be theoretically reliable. In practice, however, they have been
found to have quite low statistical power. Consequently, even
when a particular exchange rate follows martingale behavior,
the null hypothesis can sometimes be rejected. Among the tests
that rely on alternative representations of the autocorrelogram
of the return series are the VR test (Cochrane 1991; Lo and
MacKinlay 1988), the Fama and French (1988) regression test,
and the Jegadeesh (1991) regression test.
What differentiates Lo and MacKinlay’s VR test from others [mainly from the one used by Cochrane (1991) and Poterba
and Summers (1988)] is that it is possible to conduct the test
even when stock returns are heteroscedastic. The VR test statistic is a weighted sum of estimated autocorrelation coefcients,
with the weights declining in the return horizon. Being a twotailed test, rejection by the VR test reveals information about
autocorrelation structure. If the VRs at different return horizons are greater (smaller) than 1, then one can condently conclude that stock returns are positively (negatively) correlated.
Accordingly, a value of 1 for the VR means that stock prices
follow random walk. Random-walk series have a unit root, and
random-walk increments are required to be uncorrelated. Lo
and MacKinlay (1988) examined the VR, Dickey–Fuller, and
Box–Pierce tests and found that the VR test was more powerful
than the others under the heteroscedastic random-walk model.
Lo and MacKinlay (1988) used the idea behind VRs to test
for independently and identically distributed (iid) Gaussian increments rst, and then extended it to the case with uncorrelated
but heteroscedastic increments. Lo and MacKinlay’s Monte
Carlo power tabulations showed that the VR test yielded higher
power under both approximations compared to the Dickey–
Fuller t test and the Box–Pierce portmanteau Q test. The VR
test is preferred when the focus is the absence of correlation
among the increments.
Lo and MacKinlay’s VR test procedure can be applied when
returns are heteroscedastic, given that they are uncorrelated
with each other. If the increments are uncorrelated, then the
sum of the variances of the increments should be equal to the
sum of their variances, and the VR should move closer to 1
even with heteroscedastic disturbances. The asymptotic variance will depend on the degree and type of heteroscedasticity
present. Rather than specifying the form of heteroscedasticityin
increments, Lo and MacKinlay (1988) followed White (1980)
in deriving variance VRs that allow for general forms of heteroscedasticity. They made use of the relationship between the
VR and autocorrelation coefcients to derive the asymptotic
distribution of the VR estimator under heteroscedastic disturbances.
Lo and MacKinlay’s heteroscedasticity-consistent VR test
statistic, z¤ .q/, is used to test the null hypotheses for a specic aggregation value (holding period), q. If z¤ .q/ is greater
than the critical value of the standard normal distribution, then
the random-walk hypothesis is rejected. However, because VRs
may be statistically close to 1 for some q and different from
1 for others, the VR test procedure based on various holding
periods can easily lead to inconclusive results.
Chow and Denning (1993) proposed a solution to this problem. They used Hochberg’s (1974) theorem on MCTs and
extended the Lo–MacKinlay VR test to incorporate multiple
comparisons of selected VRs with 1. Taking k VR test statistics, z¤ .qi /s, for i D 1; 2; : : : ; k, that have standard normal
distribution under the random-walk null hypothesis, and using
a Bonferroni probability inequality, the Hochberg (1974) test
amounts to picking up the test statistics z¤ .qi / with the largest
absolute value. Hochberg (1974) showed that the largest absolute value of these k standard normal variates has a studentized maximum modulus (SMM) distribution with k and nq
(sample size) degrees of freedom. The critical values for the
SMM distribution are greater than the critical values for the
standard normal distribution. This is not surprising given that
the MCT statistic is the maximum of the VR test statistics for
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
all selected holding periods. The critical values of the SMM
distribution were provided by Hahn and Hendrickson (1971).
The other joint VR test used in this article was developed
by Richardson and Smith (1991) and makes explicit use of the
serial correlation among VRs when the observations used to
calculate VR overlap. If one wants to calculate the VR for a
4-day holding horizon using a sample of 100 observations, then
he or she would either have 25 nonoverlappingobservations or
97 overlappingobservations for 4-day returns. Obviously,using
overlapping observations will substantially increase the sample
size from which to calculate VRs. However, the distribution of
VRs of different return horizons calculated from overlapping
data is likely to be nonnormal, because of the serial correlation
among the VRs. For a given number (say m) of VRs with different return horizons, Richardson and Smith (1991) derived a
Wald test procedure to test for the null hypothesis which explicitly takes into account the serial correlation among m VRs.
4.
TEST RESULTS: FULL-SAMPLE
AND FIXED-LENGTH
MOVING-SUBSAMPLE WINDOWS
Our dataset includes daily exchange rates for January 2,
1974–February 12, 2001. The data are downloaded from the
Federal Reserve Bank of Chicago’s website (http://www.frbchi.
orgeconinfo/nance/for-exchange/welcome.html) and cover the
period January 1971–February 2001. Because many countries
switched to a oating exchange rate regime in the period 1971–
1973, following earlier literature, the sample here is restricted
to the period January 1, 1974–February 12, 2001. The same
tests were conducted also including the data for the 1971–1974
period, and no qualitative change was found in the results.
The analysis used daily, rather than weekly, exchange rates
for two reasons. First, the literature on FX market interventions
emphasizes that the effects of interventions occur immediately
and diminish monotonically over time (Dominquez 1990). Using weekly exchange rates would preclude capturing the immediate effects of the interventions. Second, unlike the case with
stock returns, using daily exchange rates avoids the problem of
spurious correlation caused by infrequent trading. As discussed
earlier, the FX markets are very liquid. Because the tests are
being applied on exchange rate returns and not on stock market
index returns (which are composed of dozens of stocks, some
of which may be traded infrequently), the daily exchange rates
can be used without much worry.
The empirical analysis herein focuses on daily exchange
rates of the US$ against seven major currencies: DEM, JPY,
CHF, FRF, GBP, ITL, and CD$. Fixed-length moving windows
389
with 1,000 daily observations are considered. A window length
of 1,000 days is chosen to ensure that the results will not suffer
from small sample bias and will be comparable with the results
of Liu and He (1991) and Fong et al. (1997), which had 785
observations in their samples.
The rst subsample window starts on January 2, 1974 and
ends on December 29, 1977. After the joint VR test statistic
for the rst subsample is calculated, the window is moved ve
daily observations forward, and the joint VR test statistic is recalculated. (It was decided to increase the sample size by ve
daily observations at a time to save on computer time.) Once
the test statistics for all windows are obtained, they are plotted,
and their behavior over time is analyzed.
Before the test results for moving windows are reported, Table 3 presents descriptive statistics to highlight some characteristics of daily exchange rates throughout the January 1974–
February 2001 period. Based on the average daily log exchange
rate changes, it can be concluded that on average, US$ has
depreciated against DEM, JPY, and CHF and has appreciated
against GBP, FRF, CD$, and ITL. Daily exchange rate changes
are not skewed one way or the other. All exchange rates have
leptokurtic distribution. This is the reason behind the rejection
of normality of daily log exchange rate changes by the Jarque–
Berra test reported in the Table 3.
Table 4 presents the VRs along with the RS test and the
heteroscedasticity-consistent multiple comparison test for the
full sample using 2-, 4-, 8-, and 16-day return horizons. As
the return horizon further increases, the number of nonoverlapping observations (1,000/return horizon) will decrease. Lo and
MacKinlay (1989) showed that this will lead to a decline in the
power of the VR test. For this reason, return horizons longer
than 16 days are not considered. However, checked whether
our results are sensitive to the choice of return horizon was
checked, and it was determined that the results do not change
signicantly when longer return horizons were included in the
calculation of test statistics.
The VRs for all currencies are greater than 1, indicating the
possibility of positive serial correlation in daily innovations to
exchange rates. The MCT rejects the martingale property for
the exchange rate of US$ against DEM, JPY, GBP, FRF, and
CD$ at the 10% signicance level. The RS Wald test rejects
the martingale hypothesis for these exchange rates at either the
5% or the 1% signicance level. It rejects the null hypothesis
for the ITL exchange rate as well. Rejection of the martingale
property for these currencies is not due to long return-horizons;
the longest return-horizon considered is 16 days—much shorter
than the size of the subsample windows.
Table 3. Descriptive Statistics for Daily Log Exchange Rate Changes (January 1974–February 2001)
Mean
Median
Maximum
Minimum
Standard deviation
Skewness
Kurtosis
Jarque-Bera
DEM
JPY
¡:00004
¡:00013
US$/GBP
¡:00007
FRF
0
0
0
0
0
0
0
:0587
¡:0414
:0066
:0087
6:324
3;133
:0626
¡:0563
:0066
¡:3943
8:740
9;519
:0459
¡:0384
:0062
¡:1232
6:839
4;197
:0587
¡:0391
:0064
:1341
7:966
7;015
:1035
¡:0972
:0077
:0417
14:099
34;944
:0669
¡:0404
:0063
:4379
10:404
15;765
:0190
¡:0186
:0027
:1533
6:717
3;946
:00006
CHF
¡:00010
ITL
CD$
:00018
:00006
390
Journal of Business & Economic Statistics, July 2003
Table 4. VR Test for Daily Log Exchange Rate Changes (January 1974–February 2001)
VR test statistic (z ¤ )
VR
DEM
JPY
GBP
FRF
CHF
ITL
CD$
2 days
4
8
16
1:03
1:036
1:061
1:03
1:008
1:042
1:061
1:044
1:061
1:087
1:051
1:004
1:063
1:074
1:078
1:091
1:118
1:091
1:007
1:081
1:083
1:149
1:2
1:147
1:149
1:048
1:151
1:111
4
8
16
RS test
p value
1:563
1:85
2:927
1:819
:079
1:76
2:336
1:758
1:838
2:521
2:048
:12
1:49
1:715
2.30¤
2.85¤¤
2.136
2.29¤
.595
1.997
1.601
:0159¤¤
ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20
Martingale Property of Exchange Rates and
Central Bank Interventions
Kamil Yilmaz
To cite this article: Kamil Yilmaz (2003) Martingale Property of Exchange Rates and
Central Bank Interventions, Journal of Business & Economic Statistics, 21:3, 383-395, DOI:
10.1198/073500103288619034
To link to this article: http://dx.doi.org/10.1198/073500103288619034
View supplementary material
Published online: 01 Jan 2012.
Submit your article to this journal
Article views: 57
View related articles
Citing articles: 4 View citing articles
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ubes20
Download by: [Universitas Maritim Raja Ali Haji]
Date: 13 January 2016, At: 01:03
Martingale Property of Exchange Rates
and Central Bank Interventions
Kamil Y ILMAZ
College of Administrative Sciences and Economics, Koç University, Rumelifeneri Yolu,
Sariyer 34450, Istanbul, Turkey (kyilmaz@ku.edu.tr )
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
This article uses the variance ratio-based multiple comparison test and the Richardson–Smith Wald test
procedures to test for the martingale property of daily exchange rates of seven major currencies vis-à-vis
the U.S. dollar. To allow for the possibility that exchange rates are not governed by a single process
throughout the oat, the test statistics are calculated and plotted for xed-length moving subsample windows rather than being applied to the full sample. The results show that exchange rates do not always
follow the martingale process. During the times of coordinated central bank interventions, exchange rates
deviate from the martingale property.
KEY WORDS: Fixed-length moving subsample window; Joint variance ratio test; Multiple comparison
test; Richardson–Smith Wald test.
1.
INTRODUCTION
Since the breakdown of the Bretton Woods system in the
early 1970s, exchange rate economics has become an area of
active research for economists. Earlier, the focus was more on
structural models to explain exchange rate behavior over time.
However, since Meese and Rogoff (1983) showed that the structural models had inferior performance than a naïve martingale
in out-of-sample forecasts, many studies strived to uncover the
empirical regularities in exchange rate behavior.
Baillie and Bollerslev (1989) found evidence supporting the
presence of cointegration among 7 major daily exchange rates
during the period between 1980 and 1986. However, Diebold,
Gardeazabal, and Yõlmaz (1994) showed that the results obtained by Baillie and Bollerslev (1989) were sensitive to the
inclusion of a drift in the tests, which happened to be in the
data during the 1980–1986 period. Once the drift is included,
evidence turns against the cointegration, and the random walk
performs better than alternative models in out-of-sample forecasts.
Applying the variance ratio (VR) test to weekly exchange
rates between August 1974 and March 1989, Liu and He
(1991) rejected the martingale hypothesis for the German mark
(DEM), Japanese yen (JPY), and British pound (GBP), but
failed to do so for the Canadian dollar (CD$) and French franc
(FRF) vis-à-vis the U.S. dollar (US$). In a recent follow-up,
Fong, Koh, and Ouliaris (1997) emphasized the shortcomings
of Liu and He’s analysis. They studied the statistical performance of two different multiple VR tests of the martingale hypothesis: Hochberg’s (1974) multiple comparison test (MCT)
and Richardson and Smith’s (1991) (RS) Wald test. Then they
applied these tests to exchange rates over the October 1979–
March 1989 period. They found that the RS test failed to reject
the martingale hypothesis for all ve exchange rates considered, whereas the MCT continued to reject the hypothesis for
the FRF, DEM, and JPY.
Tests of the martingale hypothesis are related to the correlogram of log exchange rate increments. They evaluate whether
the autocorrelation coefcients at different lags and leads
equal 0. Liu and He (1991) and Fong et al. (1997), among others, conducted tests of martingale property in nancial time
series for a given time period and reached a verdict about the
behavior of the asset prices during that period. However, it is not
correct to assume that the process that governs the time series
behavior of exchange rates stayed unchanged during a 25-year
period. Central bank interventionsin the foreign exchange (FX)
markets or the frequent realignments in the exchange rate mechanism of the European monetary system (EMS) are some factors that might possibly have affected the behavior of exchange
rates over time. For example, Dominquez (2001) provided evidence that central bank interventions inuence intradaily FX
returns and volatility.
Given the fact that central banks of major industrial countries
have changed their stance with respect to market intervention
over time, there is a possibility that policy shifts can result in
a change in the time series behavior of exchange rates. For example, as Dominquez (1998) stated; after 4 years of passive
intervention policy between 1981 and 1984, the Federal Reserve became more active toward the end of 1985 to slow down
the appreciation of the dollar against other major currencies.
These shifts in the policy stance must be taken into account.
One alternative then is to assume a priori that there is a structural break in the data. For example, taking into account the
changes in the Federal Reserve’s operating procedures, Liu and
He (1991) treated October 1979 as a structural breakpoint and
divided their sample in two. This is a step in the right direction,
but it still falls short of a satisfactory solution for the problem at
hand. Even if a change occurs in the time series behavior of exchange rates, this does not have to be a signicant discrete jump
in the underlying parameters. As long as the change takes the
form of a slow, continous process or a small jump in the parameters, structural break tests are unlikely to capture the change
(Diebold and Chen 1996).
In this article it is suggested that tests of the martingale property in exchange rates need to control for the sensitivity of the
results to the particular sample period used. For that reason,
tests of the martingale property were conducted in movingsubsample windows with a xed length of 1,000 daily observations. The test statistics for all subsample windows are plotted. Plotting the test statistics for subsample windows facilitates
383
© 2003 American Statistical Association
Journal of Business & Economic Statistics
July 2003, Vol. 21, No. 3
DOI 10.1198/073500103288619034
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
384
Journal of Business & Economic Statistics, July 2003
observation of whether there is any change in the behavior of
exchange rates over time.
Following Fong et al. (1997), the present work uses two joint
VR test procedures. These are the MCT proposed by Chow and
Denning (1993) and the joint VR test developed by Richardson and Smith (1991). These tests are applied to changes of
daily New York spot exchange rates of the U.S. dollar vis-à-vis
seven major currencies: the DEM, JPY, GBP, FRF, Swiss franc
(CHF), CD$, and Italian lira (ITL). The sample period starts on
January 1, 1974 and ends on February 12, 2001.
This article is not an attempt to develop a theory that shows
how the martingale property can be rejected after the central
bank interventions. However, theoretical models can be used
to establish the link between the monetary policy actions and
the violation of the martingale. McCallum (1994) and Meredith and Chinn (1998) presented theoretical models showing that
the violation of the uncovered interest parity (UIP) can be due
to the presence of feedback mechanisms between the exchange
rates, ination, output, and interest rates. Under the assumption
that the daily risk-free interest rate is 0, which is not a totally
unjustied approximation with daily data, the UIP implies that
the daily exchange rate is a martingale. Based on this assumption, it is theoretically possible for the monetary policy feedback mechanisms to cause daily exchange rates to deviate from
martingale behavior.
The article is organized as follows. Section 2 briey reviews
the developments in the foreign exchange markets since the
oat, as well as the literature on exchange rate behavior. Section 3 provides a detailed account of the joint VR tests used in
the analysis, and Section 4 presents the empirical results. Section 5 concludes by summarizing the results.
2.
EXCHANGE RATES UNDER THE FLOAT:
THE MARKET, CENTRAL BANK
INTERVENTIONS, AND THE LITERATURE
2.1
Foreign Exchange Markets
Established as an informal market in the 1960s, FX markets
grew rapidly in the 1980s and especially in the 1990s. Accord-
ing to surveys conducted by the Bank for International Settlements (BIS) every 3 years, since April 1989 average daily
turnover in foreign exchange markets worldwide (adjusted for
cross-border and local double-counting and evaluated at April
1998 exchange rates) increased by 33%, 29%, and 46% between consecutive triennial surveys.
The U.S. dollar has been the dominant currency in both the
spot and the forward and swap transactions. Its share in daily
turnover has uctuated between 80% and 90% (when reported
on one side of the transactions). The sum of the remaining six
major currencies (all included in our analysis) accounts for a
market share approximately equal to that of the U.S. dollar. The
remaining 20%–30% of the total (200%) market turnover has
been accounted by other currencies from Europe and as well as
from other parts of the world (Table 1).
BIS surveys also include information on the liquidity of bilateral FX transactions. U.S. dollar bilateral exchange rates against
six major currencies in the sample herein form the most liquid
segments of the FX market. For example, 63% of average daily
trade volume in April 1998 was accounted by the bilateral U.S.
dollar transactions against other major currencies included in
our analysis, except ITL.
The data used in this article are reported noon spot exchange
rates in New York. For that reason, it is quite relevant to study
the turnover of each currency in the New York market. Table 1
reports the average daily turnover in 1995 for the seven major
currencies in the New York market in their respective base markets and the world market as a whole.
Based on this data, the currencies can be classied into three
groups. With $104 and $55 billion daily turnovers, the DEM
and JPY are the two most actively traded currencies in the
New York market after the US$. Next are the three European
currencies (the GBP, FRF, and CHF), each with an approximate $20 billion daily turnover. Finally, the daily turnovers for
the CD$ and Australian dollar (AU$) are less than $10 billion.
Table 1 reveals that spot markets went through a rapid expansion in the rst half of the 1990s. Whereas on average only
$140 billion worth of currency changed hands daily in 1992,
according to BIS surveys this amount increased to more than
Table 1. Total Daily Turnover in FX Markets
April 1992
US$/DEM
US$/JPY
US$/GBP
US$/CHF
US$/CD$
DEM/GBP
US$/FRF
DEM/JPY
US$/AU$
DEM/CHF
Other
Total
April 1995
Total
(bil $)
Share in
total (%)
Of which
spot (%)
192:2
154:8
76:5
48:8
25:4
23:3
18:6
18:2
17:9
13:3
195:9
784:9
24
20
10
6
3
3
2
2
2
2
25
30
16
9
6
2
5
1
4
1
3
23
Total
(bil $)
US$/DEM
253:9
US$/JPY
242
US$/othEMS
104:3
US$/GBP
77:6
US$/CHF
60:5
US$/FRF
60
DEM/othEMS
38:2
US$/CD$
38:2
DEM/FRF
34:4
US$/AU$
28:7
DEM/JPY
24
DEM/GBP
21:3
DEM/CHF
18:4
Other
135:4
Total
1136:9
April 1998
Share in
total (%)
Of which
spot (%)
22
21
9
7
5
5
3
3
3
3
2
2
2
12
56
36
33
37
17
32
86
31
79
86
Total
(bil $)
US$/DEM
290:5
US$/JPY
266:6
US$/othEMS
175:8
US$/GBP
117:7
US$/CHF
78:6
US$/FRF
57:9
US$/CD$
50
US$/AU$
42:2
DEM/othEMS
35:1
DEM/GBP
30:7
DEM/JPY
24:2
DEM/CHF
18:4
US$/XEU
16:6
Other
237:2
Total
1441:5
Share in
total (%)
20
18
12
8
5
4
3
3
2
2
2
1
1
16
Of which
spot (%)
49
45
14
33
30
16
25
33
75
79
77
NOTE: After adjusting for double counting in interbank transactions, the average daily turnover in the New York market was 26.1 billion per day in April 1983. Other currencies in the EMS are
denoted by othEMS.
Source: Bank of International Settlements (1992, 1995, 1998).
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
$500 billion in 1995. The expansion of the spot FX markets
continued in the second half of the 1990s, although with some
slowdown. Whereas total daily FX market turnover increased
by 27% from 1995 to 1998, most of this increase was due to the
expansion in the forward FX markets. Daily total spot market
turnover increased by only 14%, to $590 billion.
Comparable gures for the 1970s and 1980s are not available. However, it is evident from the available data that the FX
markets have gone through a period of rapid expansion in the
1990s.
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
2.2
Central Bank Interventions
Especially in the earlier years of the oat, FX markets have
gone through periods of instability. All major industrial countries were affected adversely by oil crises in 1973 and 1979.
The oil price hikes not only disturbed their external balances,
but also led to high ination rates never before seen in these
countries in the postwar period. The impact on the relative values of major currencies was unprecedented, leading to subtantial volatility in the foreign exchange markets. Due to increased
inationary pressures and rapid decline in the political power of
the Carter administration, toward the end of the 1970s, the U.S.
dollar started to lose value against other major currencies.
In the rst 2 years of the oat central banks intervened sporadically with no coordination. The intervention was seen as a
necessary policy tool to stabilize highly volatile FX markets.
However, in October 1974 the U.S. Federal Reserve, the German Bundesbank, and the Swiss National Bank began intervening in a concerted fashion to control the volatility of the DEM
and CHF exchange rates (Schwartz 2000). The coordinated interventions continued throughout the 1970s, with the participation of the Bank of Japan after September 1977. But despite the
U.S. interventions, the U.S. dollar continued to depreciate until
1980.
Differences among industrial countries’ responses to oil price
shocks continued to shape the policy issues and debates in the
1980s. To bring ination under control, the Federal Reserve began to follow a tight monetary policy in 1980. The resulting
high interest rates attracted capital inows to the United States,
leading to the appreciation of the U.S. dollar. The appreciation
of the dollar lasted until 1985, and at its peak in late February and early March 1985, the dollar was overvalued by 40%
(Obstfeld 1990).
After coming to power in 1981, the Reagan administration
followed a policy of little intervention. It refused any coordinated intervention in FX markets except in an emergency case.
The concerted interventions that occurred for a short period
in June–August 1982 were consistent with this policy stance.
However, faced with ever rising dollar for over 4 years, the U.S.
government could not stick to its promise and had to search for
coordination among major central banks.
The period 1986–1991 was a time of concerted interventions
in FX markets around the world. In September 1985, G-7 nance ministers agreed to intervene in the worldwide FX markets in a concerted fashion when they nd it necessary. This
agreement, known as the Plaza Accord, marked a drastic change
in the policy stance of the major central banks in terms of the
movements of exchange rates. Soon after the signing of the
385
Plaza Accord came a heavy bout of concerted interventions.
Most of the interventions took the form of selling U.S. dollars
against other major currencies, especially against the DEM and
the JPY.
These interventions paid off; the US$ started to lose much
of the value that it had gained against other currencies, thanks
in large part to the massive sterilized interventions by the Federal Reserve, the Bundesbank, and the Bank of Japan. These interventions were effective in signaling the policy stance of the
monetary authorities and thus could lead to some predictable
changes in the exchange rates during the second half of 1980s
(Dominquez 1990).
After the success of the Plaza Accord, leading central
bankers continued to work closely to prevent wide swings in
the exchange rates. The Louvre Accord of February 1987 was
an explicit step in this direction. It set unannounced and secret
target bands for the DEM/US$ (between 1.6 and 1.9) and the
JPY/US$ (between 120 and 140) exchange rates, beyond which
central banks had agreed to intervene.
According to Catte, Galli, and Rebecchini (1994), the leading central banks had undertaken 17 concerted interventions
between 1985 and 1991. The U.S. Federal Reserve, the Bundesbank, and the Bank of Japan were the major players in
every intervention. During this period, none of the G-3 central
banks undertook any intervention contradicting the policies of
the other two. McKinnon (1996, pp. 67–68) emphasized that 16
out of 17 interventions during this period could be desribed as
“leaning against the wind.”
Contrary to the implications of the theory, there is consensus among economists on whether central bank interventions
have some lasting effects on FX markets. In the absence of
an explicit coordination, these interventions had to be sterilized to keep the monetary stability intact. Baillie and Osterberg
(1997) showed that in the 1980s, the effects of sterilized interventions lasted beyond the day of intervention. Dominquez
(1990) showed that the effects of sterilized intervention diminish monotonically over time, and that concerted interventions
are more effective than individual interventions in generating
the desired exchange rate behavior.
McKinnon (1993) claimed that these infrequently exercised,
explicitly announced concerted interventions affected the FX
markets, simply because they signaled the policy stance of the
major central banks and, thus inuenced the expectations about
the future behavior of exchange rates. Obstfeld (1990), on the
other hand, claimed the contrary. Based on anecdotal evidence,
he argued that sterilized interventions were effective only when
backed by appropriate monetary policy adjustments. Together,
these studies show that changes in FX monetary, or scal policies do have some lasting impact on FX markets.
In addition to these studies, Dominquez (1998) showed that
central bank interventions on average led to higher volatility in
bilateral DEM/US$ and JPY/US$ exchange rates. With a value
of 6.14, the maximum conditional volatility for DEM/US$ occurred in November 2, 1978, soon after the Carter administration’s decision to intervene in markets to support a declining
U.S. dollar. In the case of the JPY/US$ exchange rate, the maximum volatility was 3.27, observed just 2 days after the Plaza
Accord was signed.
Because not all of the central banks were involved in all of
the concerted policy interventions, market interventions cannot
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
386
Journal of Business & Economic Statistics, July 2003
be expected to affect bilateral exchange rates of the U.S. dollar
vis-à-vis all other major currencies. Being the issuers of most
traded currencies, the Federal Reserve, the Bundesbank,and the
Bank of Japan intervened selectively to affect the value of the
US$ vis-à-vis the DEM, JPY, and, to some extent, GBP. Consequently, if policy interventions do have lasting impact, then
these bilateral exchange rates are relatively more likely to diverge from martingale behavior during the period of concerted
policy interventions.
In comparison to the 1980s, throughout the 1990s fewer FX
market interventions occurred. According to news reports, interventions of the 1990s are in general smaller in magnitude
than those of the previous decade. Nine relatively small-scale
interventions were undertaken between 1991 and 1999 (Table 2). One important reason behind this change was the relative calm in the FX markets around the world in the 1990s. The
large swings that characterized the FX markets in the 1980s,
especially when the U.S. dollar was concerned, were not observed in the 1990s; therefore, the need for policy intervention
occurred less frequently and at a smaller scale.
The only exception to the relative calm of the 1990s was the
ERM crisis of September 1992. After excessive speculative attacks, the GBP, ITL, and the Swedish kroner dropped out of
the ERM and were allowed to oat freely since then. During
the ERM crisis, central banks of the respective countries intervened heavily to defend their ERM exchange rates. The nancial crises in Mexico, East Asia, and Russia did not have
any major impact in the worldwide FX markets for major currencies and thus did not necessitate policy intervention by the
central banks of the G-7 countries. Recently, calls for concerted
intervention intensied after the apparent failure of the Euro to
recover its losses against the U.S. dollar after the Euro’s inauguration in January 1999.
2.3
Literature on the Martingale Property
of Exchange Rates
Since the breakdown of the Bretton Woods system, numerous
studies on the behavior of exchange rates under the oat have
been reported. The work of Meese and Rogoff (1983) has been
among the most inuential. Using short-horizon log exchange
rate changes, these authors showed that the structural models
of exchange rate determination (i.e., the exible-price monetary model, the sticky-price monetary model, and the portfoliobalance model) do not perform better than the random-walk
model in out-of-sample forecasts.
Using more recently developedcointegrationtest procedures,
Baillie and Bollerslev (1989) found evidence supporting the
presence of cointegration among seven major daily exchange
rates during the period 1980–1986. A nding of cointegration
would mean a long-run equilibrium relationship between exchange rates. Short-run deviations from this long-run equilibrium relationship (called the error-correction model) can be predicted. Using a maximum likelihood–based Johansen test procedure, Diebold et al. (1994) showed that the results obtained
by Baillie and Bollerslev (1989) were sensitive to the inclusion of a drift in the tests, which happened to be in the data
during the 1980–1986 period. Once the drift is included, evidence turns against the cointegration. Diebold et al. (1994) also
showed that the random walk performs better in out-of-sample
forecasts compared with alternatives such as error-correction
model that would be implied by the presence of cointegration
and unrestricted vector autoregression (VAR).
Besides the studies focusing on short-horizon log exchange
rate changes, a whole set of studies provides direct and indirect evidence against random-walk behavior at long horizons.
First, a series of panel studies show that purchasing power parity, an alternative to random-walk behavior, holds in the long
run but not in the short run (Lothian 1996, Papell 1997). Second, using long-horizon changes, Lothian and Taylor (1996)
showed that the real exchange rate mean reverts and that univariate rst-order autoregressive models perform better than alternative random-walk models both before and after the oat.
Third, Mark (1995), Chinn and Meese (1995), and Mark and
Sul (2001) found that exchange rate deviations from monetary
fundamentals predict future exchange rates. Finally, Meredith
and Chinn (1998) showed that uncovered interest parity may
hold over long horizons, but not over short horizons.
Without a doubt, these results provide evidence that at long
horizons, exchange rates do not follow random-walk behavior.
Placed against the evidence supporting random-walk behavior
at short horizons, this result raises a serious question: Because
the long-horizon log exchange rate change is the sum of shorthorizon changes, it is surprising that there is little evidence
against the random walk over short horizons. In this regard, this
article should be viewed as an attempt to reconcile results of the
short-horizon tests with those of the long-horizon tests.
Attempts have been made to use semiparametric procedures
to test for the martingale property of exchange rates. The main
problem with these tests arises if the null hypothesis is rejected,
in which case there is no way to determine the alternative hypothesis. Liu and He (1991) applied the VR test for the martingale property on ve major exchange rates (DEM, JPY, GBP,
CD$, and FRF) against the US$ over the sample period August
1974–March 1989. They used the VR test and rejected the martingale property for the DEM, JPY, and GBP, but failed to do
so for the CD$ and FRF vis-à-vis the US$ for weekly exchange
rates.
Fong et al. (1997) studied the statistical performance of
two different multiple VR tests of the martingale hypothesis:
Hochberg’s MCT and the RS Wald test. Fong et al. (1997) took
their analysis one step further and applied the multiple VR test
and the RS Wald test to the same data. They started by showing that in small samples, the RS Wald test had better power
properties than the multiple VR test. When they applied both
tests to the October 1979–March 1989 period, the RS Wald test
failed to reject the martingale hypothesis, whereas the multiple
VR test continued to reject the hypothesis for the FRF, DEM,
and JPY.
All studies testing the martingale property of exchange rates
were based on a xed sample period. This sample period is dictated either by the availability of the data or by visible breaks,
such as a switch in the monetary or exchange rate policy in
the country of interest. For example, Liu and He (1991) divided their sample into 1974–1978 and 1979–1989 to take
into account a major change in U.S. monetary policy. In their
analysis of the implications of the European ERM on the exchange rate dynamics, Anthony and MacDonald (1998) divided
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
387
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Table 2. Chronology of Events Concerning the FX Markets
Date
Event
October 1978
Feb–Apr 1979
March 1979
Sep 23, 1979
Nov 30, 1979
Nov 1979–Jan 1980
Feb–Apr 1980
Mar 02, 1980
Mar 17, 1980
FED bought US$.
Central banks’ total intervention in this period amounted to $38 bil.
Inception of the ERM.
ERM realignment (ERM re): FRF devalued.
ERM re: ITL devalued.
Central banks’ total intervention in this period amounted to $24 bil.
Central banks’ total intervention in this period amounted to $37 bil.
Bank of Japan’s (BoJ) 5-point plan to support yen.
Coordinated Intervention (CI): BoJ, Bundesbank (BuBa) and
Swiss National Bank (SNB) sold $300 mil.
ERM re: ITL devalued by 6%.
FED bought $500 mil.
No-intervention policy announced by the Reagan administration.
French Central bank intervened.
No intervention by the FED in this period.
BoJ sold $1 bil.
Bundesbank sold $12.8 mil.
Canada Central bank sold US$.
Swiss and four other Central banks sold $100 mil.
ERM re: FRF and ITL down by 3%, DEM and NLG up by 5.5%.
French Central bank hiked interest rates to protect franc.
ERM re: FRF, ITL fall in value; DEM, NLG up.
FED intervened.
Canada Central bank: bought C$1.6 bil.
FED intervened.
CI: DEU, JPN, CHE, NLD, GBR Central Banks sold $1 bil.
FED intervened.
FED intervened.
ERM re: Down: FRF (2.5%), ITL (2.5%), Irish Punt, IRP (3.5%);
Up: DEM (5.5%), NLG (3.5%), DNK (2.5%), BFR and LFR (1.5%).
CI: Central banks sold 2.5–3 bil.
Bank of Canada raised interest rates to protect the value of Canadian dollar.
Bundesbank sold US$.
CI: sold $1–2 bil.
Ohio bank crisis.
ERM re: ITL devalued.
Plaza Accord: Central banks sold $7 bil (between Sep22–Oct31).
Bank of Canada sold US$850 mil.
BoJ: mild intervention.
ERM re: FRF down by 3%, DEM and NLG up by 3%.
BEF, LFR and DNK up by 1%, ITL down.
ERM re: BFR, LFR fall in value; DEM, NLG up.
Louvre Accord: Central banks bought $3.5 bil between Mar 23–Apr 17.
CI: Central banks bought $4.06 bil.
FED bought $4.14 bil.
Interest rate cut by major European countries to stem the fall of the US$.
G-7 nance min reiterated their resolve to keep the US$ from falling further.
FED bought $818 mil.
FED mild int; BoJ inervened heavily to stop yen’s appreciation.
CI: Massive intervention.
CI: Central banks sold $2.93 bil.
CI: BoJ bought $1 bil; others $1 bil (FED sold JPY&DEM).
CI: Central banks sold US$.
CI: Central banks sold $10 bil.
CI: Central banks sold US$.
ERM re: ITL devalued against DEM.
CI: Central banks sold US$.
British pound joined the ERM.
CI: Central banks bought $1.5 bil.
CI: Central banks of DEU, CHE, DNK, BEL, ITA, and ESP sold US$.
US treasury announced it would act to reverse dollar appreciation.
ERM re: DNK, NLG devalued.
CI: 13 Central banks bought US$ against DEM.
Bank of England (BoE) bought GBP using 5% of its ofcial FX reserves.
BoE spent £15 bil equivalent of £44 bil FX reserves to keep
the GBP within its target band.
ERM Crisis: GBP, ITL and SWK left the EMS.
CI: FED and BoJ sold US$ to support JPY.
ERM re: Spanish Peseta and Portugese Escudo (6%) devalued.
ERM re: Irish Punt devalued.
ERM re: Spanish Peseta (8%) and Portugese Escudo (6.5%) devalued.
ERM bands expanded from 2.25% to 15%.
CI: 17 Central banks bought US$.
March 22, 1981
Mar 30, 1981
May 04, 1981
May 12, 1981
May–July 1981
July 23, 1981
Jul, 1981
Jul, 1981
August 4, 1981
Oct 4, 1981
March 25, 1982
June 12, 1982
June 14, 1982
May–June 1982
August 4, 1982
August 10, 1982
August 16, 1982
October 1982
March 21, 1983
July 29, 1983
March 15, 1984
June 25–28, 1984
Feb 27, 1985
Mar 18–20, 1985
June 20 1985
September 1985
Feb 11, 1986
Mar 18, 1986
April 6, 1986
Jan 12, 1987
Feb 21–22, 1987
Mar 22–Apr 10,1987
Nov 1987–Jan 1988
Dec 3, 1987
Dec 22, 1987
Feb–Apr 1988
Mar–Apr 1988
Apr 14–15, 1988
May–July 1988
Nov 17, 1988
Jan 11, 1989
May 22–Jun 7, 1989
Sep 24–Oct 5, 1989
Jan 8, 1990
Mar 5–7, 1990
October 1990
Feb 4–12, 1991
Mar 27, 1991
Jul 1, 1991
Apr 4, 1992
July 20–Aug 11 1992
Aug 26, 1992
Sep 14–16, 1992
Sep 17, 1992
Apr 22–27, 1993
Nov 22, 1992
Feb 1, 1993
May 13, 1993
Aug 2, 1993
May 4, 1994
(continued)
388
Journal of Business & Economic Statistics, July 2003
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Table 2. (continued)
Date
Event
Nov 2–3, 1994
Mar 2–3, 1995
Apr 5, 1995
Aug 15, 1995
Sep 22, 1995
Nov 26, 1996
Jul–Oct 1997
Jun 17, 1998
Aug 1998
Jan 12, 1999
FED bought $1.5 bil against JPY and DEM.
CI: FED, BoJ and BuBa bought $1.3 bil.
CI: FED, BoJ and BuBa bought $1 bil against JPY and DEM.
CI: FED, BoJ and BuBa bought $3 bil against JPY and DEM.
EU nance ministers’ meeting on EMU.
Italian lira rejoined the ERM.
Asian Crisis started.
CI: FED and BoJ sold $4 bil against JPY.
Russian Crisis.
BoJ bought $2–3 bil against JPY.
the 1979–1992 sample into subsamples using the date of currency’s realignment in the ERM as cutoff dates. Although this
allowed them to clean their data from the effects of the jumps in
the exchange rates during the realignment period, nevertheless
in some instances they were left with few data points (fewer
than 200 observations) to estimate VRs. However, both Lo and
MacKinlay (1988) and Richardson and Smith (1991) showed
that the VR-test has poor performance with small samples.
Moving xed-length subsample windows enables one to
identify shocks that signicantly alter the exchange rate behavior, such as the FX market interventions by central banks
and the ERM realignments in the case of European currencies.
These shocks on the exchange rate behavior are identied by
signicant jumps in the test statistic.
3.
JOINT VARIANCE RATIO TESTS
Tests of martingale hypothesis are related to the correlogram
of log exchange rate increments and evaluate whether the autocorrelation coefcients at different lags and leads are equal
to 0. Because tests of random walk do not run the risk of misspecication of the alternative hypothesis, they are expected to
be theoretically reliable. In practice, however, they have been
found to have quite low statistical power. Consequently, even
when a particular exchange rate follows martingale behavior,
the null hypothesis can sometimes be rejected. Among the tests
that rely on alternative representations of the autocorrelogram
of the return series are the VR test (Cochrane 1991; Lo and
MacKinlay 1988), the Fama and French (1988) regression test,
and the Jegadeesh (1991) regression test.
What differentiates Lo and MacKinlay’s VR test from others [mainly from the one used by Cochrane (1991) and Poterba
and Summers (1988)] is that it is possible to conduct the test
even when stock returns are heteroscedastic. The VR test statistic is a weighted sum of estimated autocorrelation coefcients,
with the weights declining in the return horizon. Being a twotailed test, rejection by the VR test reveals information about
autocorrelation structure. If the VRs at different return horizons are greater (smaller) than 1, then one can condently conclude that stock returns are positively (negatively) correlated.
Accordingly, a value of 1 for the VR means that stock prices
follow random walk. Random-walk series have a unit root, and
random-walk increments are required to be uncorrelated. Lo
and MacKinlay (1988) examined the VR, Dickey–Fuller, and
Box–Pierce tests and found that the VR test was more powerful
than the others under the heteroscedastic random-walk model.
Lo and MacKinlay (1988) used the idea behind VRs to test
for independently and identically distributed (iid) Gaussian increments rst, and then extended it to the case with uncorrelated
but heteroscedastic increments. Lo and MacKinlay’s Monte
Carlo power tabulations showed that the VR test yielded higher
power under both approximations compared to the Dickey–
Fuller t test and the Box–Pierce portmanteau Q test. The VR
test is preferred when the focus is the absence of correlation
among the increments.
Lo and MacKinlay’s VR test procedure can be applied when
returns are heteroscedastic, given that they are uncorrelated
with each other. If the increments are uncorrelated, then the
sum of the variances of the increments should be equal to the
sum of their variances, and the VR should move closer to 1
even with heteroscedastic disturbances. The asymptotic variance will depend on the degree and type of heteroscedasticity
present. Rather than specifying the form of heteroscedasticityin
increments, Lo and MacKinlay (1988) followed White (1980)
in deriving variance VRs that allow for general forms of heteroscedasticity. They made use of the relationship between the
VR and autocorrelation coefcients to derive the asymptotic
distribution of the VR estimator under heteroscedastic disturbances.
Lo and MacKinlay’s heteroscedasticity-consistent VR test
statistic, z¤ .q/, is used to test the null hypotheses for a specic aggregation value (holding period), q. If z¤ .q/ is greater
than the critical value of the standard normal distribution, then
the random-walk hypothesis is rejected. However, because VRs
may be statistically close to 1 for some q and different from
1 for others, the VR test procedure based on various holding
periods can easily lead to inconclusive results.
Chow and Denning (1993) proposed a solution to this problem. They used Hochberg’s (1974) theorem on MCTs and
extended the Lo–MacKinlay VR test to incorporate multiple
comparisons of selected VRs with 1. Taking k VR test statistics, z¤ .qi /s, for i D 1; 2; : : : ; k, that have standard normal
distribution under the random-walk null hypothesis, and using
a Bonferroni probability inequality, the Hochberg (1974) test
amounts to picking up the test statistics z¤ .qi / with the largest
absolute value. Hochberg (1974) showed that the largest absolute value of these k standard normal variates has a studentized maximum modulus (SMM) distribution with k and nq
(sample size) degrees of freedom. The critical values for the
SMM distribution are greater than the critical values for the
standard normal distribution. This is not surprising given that
the MCT statistic is the maximum of the VR test statistics for
Downloaded by [Universitas Maritim Raja Ali Haji] at 01:03 13 January 2016
Yilmaz: Martingale Property of Exchange Rates and Central Bank Interventions
all selected holding periods. The critical values of the SMM
distribution were provided by Hahn and Hendrickson (1971).
The other joint VR test used in this article was developed
by Richardson and Smith (1991) and makes explicit use of the
serial correlation among VRs when the observations used to
calculate VR overlap. If one wants to calculate the VR for a
4-day holding horizon using a sample of 100 observations, then
he or she would either have 25 nonoverlappingobservations or
97 overlappingobservations for 4-day returns. Obviously,using
overlapping observations will substantially increase the sample
size from which to calculate VRs. However, the distribution of
VRs of different return horizons calculated from overlapping
data is likely to be nonnormal, because of the serial correlation
among the VRs. For a given number (say m) of VRs with different return horizons, Richardson and Smith (1991) derived a
Wald test procedure to test for the null hypothesis which explicitly takes into account the serial correlation among m VRs.
4.
TEST RESULTS: FULL-SAMPLE
AND FIXED-LENGTH
MOVING-SUBSAMPLE WINDOWS
Our dataset includes daily exchange rates for January 2,
1974–February 12, 2001. The data are downloaded from the
Federal Reserve Bank of Chicago’s website (http://www.frbchi.
orgeconinfo/nance/for-exchange/welcome.html) and cover the
period January 1971–February 2001. Because many countries
switched to a oating exchange rate regime in the period 1971–
1973, following earlier literature, the sample here is restricted
to the period January 1, 1974–February 12, 2001. The same
tests were conducted also including the data for the 1971–1974
period, and no qualitative change was found in the results.
The analysis used daily, rather than weekly, exchange rates
for two reasons. First, the literature on FX market interventions
emphasizes that the effects of interventions occur immediately
and diminish monotonically over time (Dominquez 1990). Using weekly exchange rates would preclude capturing the immediate effects of the interventions. Second, unlike the case with
stock returns, using daily exchange rates avoids the problem of
spurious correlation caused by infrequent trading. As discussed
earlier, the FX markets are very liquid. Because the tests are
being applied on exchange rate returns and not on stock market
index returns (which are composed of dozens of stocks, some
of which may be traded infrequently), the daily exchange rates
can be used without much worry.
The empirical analysis herein focuses on daily exchange
rates of the US$ against seven major currencies: DEM, JPY,
CHF, FRF, GBP, ITL, and CD$. Fixed-length moving windows
389
with 1,000 daily observations are considered. A window length
of 1,000 days is chosen to ensure that the results will not suffer
from small sample bias and will be comparable with the results
of Liu and He (1991) and Fong et al. (1997), which had 785
observations in their samples.
The rst subsample window starts on January 2, 1974 and
ends on December 29, 1977. After the joint VR test statistic
for the rst subsample is calculated, the window is moved ve
daily observations forward, and the joint VR test statistic is recalculated. (It was decided to increase the sample size by ve
daily observations at a time to save on computer time.) Once
the test statistics for all windows are obtained, they are plotted,
and their behavior over time is analyzed.
Before the test results for moving windows are reported, Table 3 presents descriptive statistics to highlight some characteristics of daily exchange rates throughout the January 1974–
February 2001 period. Based on the average daily log exchange
rate changes, it can be concluded that on average, US$ has
depreciated against DEM, JPY, and CHF and has appreciated
against GBP, FRF, CD$, and ITL. Daily exchange rate changes
are not skewed one way or the other. All exchange rates have
leptokurtic distribution. This is the reason behind the rejection
of normality of daily log exchange rate changes by the Jarque–
Berra test reported in the Table 3.
Table 4 presents the VRs along with the RS test and the
heteroscedasticity-consistent multiple comparison test for the
full sample using 2-, 4-, 8-, and 16-day return horizons. As
the return horizon further increases, the number of nonoverlapping observations (1,000/return horizon) will decrease. Lo and
MacKinlay (1989) showed that this will lead to a decline in the
power of the VR test. For this reason, return horizons longer
than 16 days are not considered. However, checked whether
our results are sensitive to the choice of return horizon was
checked, and it was determined that the results do not change
signicantly when longer return horizons were included in the
calculation of test statistics.
The VRs for all currencies are greater than 1, indicating the
possibility of positive serial correlation in daily innovations to
exchange rates. The MCT rejects the martingale property for
the exchange rate of US$ against DEM, JPY, GBP, FRF, and
CD$ at the 10% signicance level. The RS Wald test rejects
the martingale hypothesis for these exchange rates at either the
5% or the 1% signicance level. It rejects the null hypothesis
for the ITL exchange rate as well. Rejection of the martingale
property for these currencies is not due to long return-horizons;
the longest return-horizon considered is 16 days—much shorter
than the size of the subsample windows.
Table 3. Descriptive Statistics for Daily Log Exchange Rate Changes (January 1974–February 2001)
Mean
Median
Maximum
Minimum
Standard deviation
Skewness
Kurtosis
Jarque-Bera
DEM
JPY
¡:00004
¡:00013
US$/GBP
¡:00007
FRF
0
0
0
0
0
0
0
:0587
¡:0414
:0066
:0087
6:324
3;133
:0626
¡:0563
:0066
¡:3943
8:740
9;519
:0459
¡:0384
:0062
¡:1232
6:839
4;197
:0587
¡:0391
:0064
:1341
7:966
7;015
:1035
¡:0972
:0077
:0417
14:099
34;944
:0669
¡:0404
:0063
:4379
10:404
15;765
:0190
¡:0186
:0027
:1533
6:717
3;946
:00006
CHF
¡:00010
ITL
CD$
:00018
:00006
390
Journal of Business & Economic Statistics, July 2003
Table 4. VR Test for Daily Log Exchange Rate Changes (January 1974–February 2001)
VR test statistic (z ¤ )
VR
DEM
JPY
GBP
FRF
CHF
ITL
CD$
2 days
4
8
16
1:03
1:036
1:061
1:03
1:008
1:042
1:061
1:044
1:061
1:087
1:051
1:004
1:063
1:074
1:078
1:091
1:118
1:091
1:007
1:081
1:083
1:149
1:2
1:147
1:149
1:048
1:151
1:111
4
8
16
RS test
p value
1:563
1:85
2:927
1:819
:079
1:76
2:336
1:758
1:838
2:521
2:048
:12
1:49
1:715
2.30¤
2.85¤¤
2.136
2.29¤
.595
1.997
1.601
:0159¤¤