12 I.A. Moosa, P. Silvapulle International Review of Economics and Finance 9 2000 11–30
to reflect information about changes in investors’ expectations. Another reason for the interest in the presence or otherwise of a strong price–volume relationship is
that it provides support for using technical analysis as opposed or in addition to fundamental analysis.
2
Apart from Hiemstra and Jones 1994, Fujihara and Mougoue 1997, and Abhy- ankar 1998, the available empirical evidence on the price–volume relationship is
based on conventional linear Granger causality testing. Baek and Brock 1992 have shown that these tests have low power against the nonlinear alternatives. Hence, any
test based on the assumption of linearity will fail to detect nonlinear dependence. Nonlinear dependence may be present if the price and volume are generated by
nonlinear processes: this hypothesis is theoretically plausible and empirically substanti- ated.
3
Recent work has revealed the existence of nonlinear structure in the process generating returns in financial and commodity markets. These nonlinearities are nor-
mally attributed to nonlinear transaction cost functions, the role of noise traders, and market microstructure effects Abhyankar, 1998. It is now widely accepted that the
relationship between economic and financial time series are mainly nonlinear. As a result, testing for nonlinear causal relationships between two time series has received
considerable attention in the recent literature. In this article, the nonlinear causality test proposed by Baek and Brock 1992 is used to study the price–volume relationship
in the crude oil futures market.
Further motivation for using nonlinear models is provided by Savit 1988, pp. 271–272, who argued that financial and commodity markets are likely to be examples
of dynamic systems manifesting nonlinearities. He disputes the argument that fluctua- tions in time series are random and argues instead that the fluctuations are generated
by inherent nonlinearities. The distinction between linear and nonlinear adjustment to any deviation from the equilibrium price lies in whether or not the magnitude of
adjustment is proportional to the deviation. A proportional adjustment implies a linear relationship, but this kind of adjustment cannot generate the randomness observed
in financial and commodity markets. Savit argues that nonlinear adjustment can pro- duce this kind of behavior. Hsieh 1991 put forward a similar point by arguing
that large moves in prices, which are greater than what is expected under a normal distribution, may be attributed to nonlinearities.
This article is organized as follows: We first present a discussion of the theory of the price–volume relationship, followed by a brief outline of the recent empirical evi-
dence. We then present the data and examine the time series properties of the underlying variables. This is followed by an outline of the methodology used to test for linear
causality and the results of the tests. The same follows for nonlinear causality testing.
2. The price–volume relationship: theory and empirical evidence
2.1. The theory The rationale for postulating a positive relationship between volume and absolute
price changes can be found in the basic supply and demand model. Starting from an
I.A. Moosa, P. Silvapulle International Review of Economics and Finance 9 2000 11–30 13
initial equilibrium position, a change in demand induces a price change. While the adjustment takes place, transactions are executed in response to the change in demand
until a new equilibrium price is reached. Hence, the volume of transactions rises as the price changes, regardless of the direction of this change. This line of reasoning,
as put forward by Crouch 1970, Clark 1973, and Westerfield 1973, does not tell us anything about the direction of causality.
This theory was later refined by Copeland 1974, who used the volume as a proxy for the rate of information arrival. In general there are two competing hypotheses
that explain information arrival in financial markets: the mixture of distributions hypothesis and the sequential information arrival hypothesis. According to the first
hypothesis, information dissemination is contemporaneous see for example Tauchen Pittis, 1983; Harris, 1986, 1987. The sequential information arrival hypoth-
esis allows for intermediate informational equilibria see for example Jennings et al., 1981. Karpoff 1987 claimed that the mixture of distributions hypothesis is consistent
with the empirical distribution of price changes. The sequential information arrival hypothesis implies a positive intertemporal causal relationship in both directions.
Hiemstra and Jones 1994 argued that a sequential information flow results in lagged trading volume having predictive power for current absolute price changes, and lagged
absolute price changes having predictive power for current volume. On the other hand, the mixture of distributions hypothesis implies only a positive contemporaneous
causality from volume to absolute price changes with no intertemporal causality in either direction.
While the mixture of distributions hypothesis and the sequential information arrival hypothesis consider the relevant price variable to be the absolute price change, some
economists argue that the relevant variable is the price change per se the signed price change. Ying 1966 argues that if there is asymmetry in the behavior of the
ratio of volume to price change, then what is important is the price change per se rather than the absolute price change. This postulation is supported by the observation
that volume is relatively heavy in bull markets and light in bear markets. A theoretical rationale for this proposition is provided by Epps 1975.
4
Thus, the signed contempora- neous relationship between trading volume and the price change reveals asymmetry
of trading volume in up and down markets. Karpoff 1988 and Suominen 1996 argued that the observed positive correlation between volume and price change can
be explained by the presence of differential costs in acquiring short and long positions. Because the costs of taking short and long positions in futures markets are identical,
asymmetry should not be observed in these markets. On the other hand, an intertempo- ral relationship has implications for market efficiency. Specifically, intertemporal cau-
sality from volume to price changes implies informational inefficiency. If this is the case, then it may be possible to make abnormal profit, which explains interest in the
price–volume relationship.
The price–volume relationship can also be explained in terms of the noise trading model of De Long et al. 1990. This model postulates that the activity of noise traders
is not based on economic fundamentals and therefore results in a temporary mispricing. The price, however, moves toward its mean value in the long run in the absence of the
14 I.A. Moosa, P. Silvapulle International Review of Economics and Finance 9 2000 11–30
transitory component. Hence, the model predicts that the positive causal relationship running from price to volume is consistent with the positive-feedback trading strategy
of noise traders who base their decisions on past price movements. Moreover, the model predicts that a positive causal relationship from volume to price is consistent
with the hypothesis that price changes are caused by the actions of noise traders. Information asymmetry is also considered by Wang 1994 in his heterogeneous inves-
tor model, which postulates that information asymmetry and investor heterogeneity may affect the price–volume relationship. As a result, trading volume is always posi-
tively correlated with absolute price change, and correlation increases with information asymmetry.
Stickel and Verrecchia 1994 explain the effect of volume on price by distinguishing between “informed” and “uninformed” trading. They present the hypothesis that
price changes are more likely to reverse after weak volume support because price changes reflect demand and higher volume reflects a greater likelihood that the
demand originates from informed rather than uninformed trading. Hence, as volume increases, the probability that the price change is information driven increases. They
provided evidence indicating that large price changes on days with weak volume support tend to reverse, at least partially.
2.2. The empirical evidence The empirical evidence on the price–volume relationship is vast and mixed. Since
the older literature is surveyed by Karpoff 1987, we will concentrate on recent evidence, particularly on the studies dealing with futures markets. These studies also
provide mixed evidence and often contradictory results. While most of them produced evidence for bi-directional causality, providing support for the sequential information
arrival hypothesis, some evidence has been found for the mixture of distributions hypothesis. On the other hand, while most of the evidence points to market inefficiency,
there is some evidence supporting efficiency, particularly in futures markets. The following is a brief description of some of the recent studies.
The evidence presented by Smirlock and Starks 1988 on stock markets and by McCarthy and Najand 1993 on currency futures markets supports the sequential
information arrival hypothesis. Furthermore, McCarthy and Najand verified the effi- ciency of the currency futures markets. Kocagil and Shachmurove 1998 examined
the same issue for 16 futures markets. The evidence on the contemporaneous relation- ship was consistent with the mixture of distributions hypothesis and the sequential
information arrival hypothesis as well as Wang’s 1994 heterogeneous investors model. The results of intertemporal analysis, however, rejected the mixture of distributions
hypothesis and provided support for the sequential information arrival hypothesis.
Hiemstra and Jones 1994 applied nonlinear causality testing to the U.S. stock market and found evidence for bi-directional causality. They also examined the propo-
sition that causality from volume to price change can be explained by volume serving as a proxy for information flow in the stochastic process generating the price change
variance. After correcting for volatility persistence in the returns, nonlinear causality from volume to price was still present.
I.A. Moosa, P. Silvapulle International Review of Economics and Finance 9 2000 11–30 15
Foster 1995 found some contrasting results by examining the price–volume rela- tionship using data from the oil futures market. Based on GARCH and GMM models,
Foster concluded that volume was not an adequate proxy for the rate of information flow but that volume and volatility were largely driven by the same factors assumed
to be information. Thus, his results support the mixture of distributions hypothesis. Moreover, he found evidence for intertemporal causality from volume to price, a
result that he did not regard as being inconsistent with the mixture of distributions hypothesis but rather indicative of market inefficiency. Foster offered two possible
explanations for inefficiency: a traders may condition their prices on previous vol- umes as a measure of market sentiment; and b it is a form of mimetic contagion,
where agents set their prices with reference to the trading patterns of other agents.
Malliaris and Urrutia 1998 examined the price–volume relationship in six agricul- tural futures contracts using cointegration and error correction analysis. They found
results in favor of bi-directional causality, such that the relationship was stronger from price to volume. These results are supported by those obtained by Fujihara and
Mougoue 1997, who examined the relationship in three oil markets. While the results of linear causality testing were inconsistent, the results of nonlinear causality testing
showed bi-directional causality.
3. Data and the time series properties of the variables
