The data and the results

438 T. Choudhry International Review of Economics and Finance 8 1999 433–453 that KPSS tests are also consistent against the stationary long-memory alternative. Harris and Inder 1994 provide the critical values required in this test.

3. The data and the results

Monthly forward and spot exchange rates from Australia, Canada, France, Ger- many, Hong Kong, Italy, Japan, South Africa, and the United Kingdom between January 1985 and December 1996 are used in the article. 20 For each country the one- month forward exchange rate is applied. All exchange rates are expressed as currency per U.S. dollar except in the case of United Kingdom where it is dollars per pound sterling. All the data are obtained from Datastream and are applied in the log form. 21 As required, before the actual cointegration tests logs of each variables were checked for unit roots. 22 Results from the ADF test, the KPSS test and the GPH test indicate all series to contain a unit root, i.e., d 5 1. These results are not provided in order to save space but are available on request. Unit roots in forward and spot exchange rates are not unique; several previous studies such as the ones cited in endnote 10 also find similar results. Table 1 presents the estimation of Eq. 1 by OLS and the estimated value of d for the equilibrium error by the GPH test. 23 In all cases, except the United Kingdom, the null hypothesis d 5 1 is rejected and the alternate null d , 1 is accepted at the 5 level or above. In other words, for all currencies except the pound sterling results indicate evidence of fractional cointegration between the one-month forward rate and the spot rate. The size of d is between 0.5 and 20.5 in all eight cointegrating relation- ships, implying mean-reverting and covariance stationary residuals. Table 2 presents the results from the Harris-Inder test where the null hypothesis is the presence of cointegration. Three different lag lengths 0, 3 and 6 are applied in this test. Cointegra- tion at all three lags are indicated for Australia, France, Germany, Japan, South Africa and the United Kingdom. In four cases, Canada, Hong Kong, Italy and the United Kingdom, conflicting results are obtained from the GPH test and the Harris-Inder test. 24 According to Harris and Inder 1994 if both the null of cointegration and no cointegration are rejected then Type I error may have occurred in one of the tests. And if both null hypotheses are accepted, then at least one of the tests lacks power against the particular data-generating process. Results from the F-test of the null hypotheses a 1 5 1 and a , a 1 5 0, 1 are provided in Table 3. Results in Tables 1 and 2 show the coefficient on the forward rate to be significant in all tests. But the null of unit coefficient on the forward rate is rejected for all currencies except the Canadian dollar and the South African rand Table 3. The null of a 5 0 and a 1 5 1 is also accepted only in the case of Canada and South Africa. In other words, the unbiased hypothesis is not rejected only in cases of Canada and South Africa. For the remaining currencies, the hypothesis is rejected at the 5 level or above. Our results provide some evidence for the weak- form forward market efficiency. The OLS estimations of Eq. 2 and the estimated value of d are shown in Tables T. Choudhry International Review of Economics and Finance 8 1999 433–453 439 Table 1 OLS estimates of s t 1 1 5 a 1 a 1 f t 1 e t 1 1 Country a a 1 Diagnostic Tests d; H : d 5 1 Australia 0.0274 0.8987 R 2 5 0.821 0.141 2.46 25.55 DW 5 1.790 23.894 a Canada 2 0.0005 0.9966 R 2 5 0.966 0.253 20.13 63.34 DW 5 2.037 23.357 a France 0.0861 0.9481 R 2 5 0.956 2 0.4617 2.81 55.32 DW 5 2.062 26.627 a Germany 0.0184 0.9591 R 2 5 0.967 2 0.2023 2.07 64.73 DW 5 2.062 25.451 a Hong Kong 0.2469 0.8797 R 2 5 0.727 0.3483 2.67 19.46 DW 5 1.660 22.955 b Italy 0.2858 0.9599 R 2 5 0.944 0.2852 2.01 48.99 DW 5 1.801 23.241 a Japan 0.1596 0.9665 R 2 5 0.980 0.2634 2.78 82.39 DW 5 1.860 23.340 a South Africa 0.0090 0.9914 R 2 5 0.973 2 0.4382 0.62 71.56 DW 5 1.740 26.521 a U.K. 0.0451 0.9156 R 2 5 0.888 0.6714 3.45 33.58 DW 5 1.804 21.490 Implies significance at the 1 level. Implies significance at the 5 level. a Implies rejection of the null d 5 1 at the 1 level. b Implies rejection of the null d 5 1 at the 5 level. t -statistics are in the parentheses. DW 5 Durbin-Watson statistics. Fractional cointegration critical values: 23.198 1, 22.245 5, 21.791 10. Source: Sephton 1995. 4 and 5. Testing Eq. 2, cointegration is confirmed in five out of the nine markets by means of the GPH test Table 4. Cointegration is rejected for Australia, Canada, Italy and the United Kingdom. Results from the Harris-Inder test are quite similar to those using the GPH test Table 5. Only the Hong Kong data provide a conflicting result; the Harris-Inder test fails to indicate a cointegrating relationship. 25 The coeffi- Table 2 KPSS Test of the Residuals Lags Australia Canada France Germany H Kong Italy Japan S Africa U.K. 0.212 0.380 b 0.098 0.095 2.645 a 0.331 b 0.129 0.113 0.150 3 0.167 0.383 b 0.100 0.096 1.640 a 0.275 c 0.110 0.087 0.136 6 0.178 0.396 b 0.110 0.109 1.224 a 0.278 c 0.112 0.130 0.148 a Implies rejection cointegration at the 1 level. b Implies rejection cointegration at the 5 level. c Implies rejection cointegration at the 10 level. KPSS critical values: 0.5497 1, 0.3202 5, 0.2335 10. Source: Harris and Inder 1994. 440 T. Choudhry International Review of Economics and Finance 8 1999 433–453 Table 3 Unbiased forward rate hypothesis test Null Hypotheses—F Statistics Country H : a 1 5 1 H : a , a 1 5 0, 1 Australia 8.294 5.325 Canada 0.047 0.800 France 9.162 7.107 Germany 7.615 5.227 Hong Kong 7.079 5.436 Italy 4.192 4.212 Japan 8.132 5.017 South Africa 0.387 0.196 U.K. 9.578 6.697 Rejection of the null at the 1 level. Rejection of the null at the 5 level. Table 4 OLS estimates of s t 1 1 5 a 1 a 1 f t 1 a 2 f t 2 1 1 e t 1 1 Country a a 1 a 2 Diagnostic tests d ; H : d 5 1 Australia 0.0291 0.9810 2 0.0881 R 2 5 0.819 1.0951 2.53 11.53 21.04 DW 5 1.876 0.431 Canada 2 0.0007 0.9472 0.0500 R 2 5 0.965 0.8208 20.18 10.96 0.58 DW 5 1.866 20.813 France 0.0952 0.9072 0.0356 R 2 5 0.952 0.4149 3.01 10.68 0.43 DW 5 1.977 22.653 c Germany 0.0208 0.9201 0.0341 R 2 5 0.965 0.3976 2.27 10.88 0.03 DW 5 1.983 22.731 c Hong Kong 0.1763 0.6644 0.2498 R 2 5 0.737 0.1956 1.87 7.34 2.77 DW 5 1.338 23.647 b Italy 0.3180 1.0630 2 0.1075 R 2 5 0.942 0.7277 2.20 12.56 21.29 DW 5 2.016 21.235 Japan 0.1746 1.0200 2 0.0566 R 2 5 0.979 0.2151 2.97 12.05 20.68 DW 5 2.000 23.559 b South Africa 0.0125 1.1070 2 0.1200 R 2 5 0.973 0.2768 0.85 13.07 21.40 DW 5 1.996 23.279 b U.K. 0.0523 0.9892 2 0.0885 R 2 5 0.881 0.7379 3.89 11.80 21.09 DW 5 2.000 21.188 Implies significance at the 1 level. Implies significance at the 5 level. Implies significance at the 10 level. b Implies rejection of the null d 5 1 at the 5 level. c Implies rejection of the null d 5 1 at the 10 level. t -statistics are in the parentheses. DW 5 Durbin-Watson statistics. Fractional cointegration critical values: 23.198 1, 22.245 5, 21.791 10. Source: Sephton 1995. T. Choudhry International Review of Economics and Finance 8 1999 433–453 441 Table 5 KPSS test of the residuals Lags Australia Canada France Germany H Kong Italy Japan S Africa U.K. 0.197 c 0.421 a 0.109 0.105 2.303 a 0.317 b 0.143 0.133 0.174 c 3 0.175 c 0.402 a 0.107 0.103 1.290 a 0.313 b 0.134 0.119 0.174 c 6 0.183 c 0.414 a 0.117 0.117 1.032 a 0.319 b 0.139 0.181 c 0.180 c a Implies cointegration at the 1 level. b Implies cointegration at the 5 level. c Implies cointegration at the 10 level. KPSS critical values: 0.5497 1, 0.3202 5, 0.2355 10. Source: Harris and Inder 1994. cient on the lagged forward rate f t 2 1 is insignificant in all tests, except in the case of Hong Kong Tables 4 and 5. Once again the null hypothesis of the unbiased hypothesis is accepted only for Canada and South Africa Table 6. But in the case of Canada we fail to find cointegration between the exchange rates. Thus, South Africa is the only country that provides evidence of a semi-strong efficient forward market. The null of a unit coefficient on the forward rate is accepted in all cases except for Hong Kong Table 6. Results from Eq. 3 estimates are presented in Tables 7 and 8. As in the first test of semi-efficiency Eq. 2 cointegration by means of the GPH test is confirmed in the same five markets. The size of the d is also similar to that in the earlier test. The Harris-Inder test provides similar results, except for the United Kingdom. Cointegra- tion is found using the dollar-pound exchange rate and the lagged spot rate as a regressor. In the previous test of the semi-efficiency we fail to confirm a cointegrating relationship using dollar-pound rates. In this particular efficiency test, the difference between the GPH test and the Harris-Inder test exists for Hong Kong and the United Kingdom. Table 6 Unbiased forward rate hypothesis test Null Hypotheses—F Statistics Country H : a 1 5 1 H : a , a 1 , a 2 5 0, 1, 0 Australia 0.050 3.809 Canada 0.373 0.699 France 1.193 5.201 Germany 0.892 3.947 Hong Kong 13.733 6.263 Italy 0.553 3.582 Japan 0.056 4.065 South Africa 0.207 0.806 U.K. 0.017 5.805 Implies rejection of the null at the 1 level. Implies rejection of the null at the 5 level. 442 T. Choudhry International Review of Economics and Finance 8 1999 433–453 Table 7 OLS estimates of s t 1 1 5 a 1 a 1 f t 1 a 3 s t 1 e t 1 1 Country a a 1 a 3 Diagnostic tests d ; H : d 5 1 Australia 0.0294 2 0.9935 1.9096 R 2 5 0.823 1.0959 2.62 21.07 2.05 DW 5 1.702 0.435 Canada 0.0096 2 1.2058 2.1751 R 2 5 0.967 0.7411 1.77 21.51 2.77 DW 5 2.008 21.174 France 0.0962 0.3514 0.5915 R 2 5 0.952 0.4150 3.03 0.31 0.51 DW 5 2.063 22.652 c Germany 0.0219 0.5338 0.4186 R 2 5 0.965 0.4094 2.27 0.49 0.39 DW 5 2.063 22.678 c Hong Kong 0.2324 2 0.4388 1.3253 R 2 5 0.851 0.1927 3.37 23.50 10.94 DW 5 2.406 23.660 b Italy 0.2909 1.9231 2 0.9646 R 2 5 0.942 0.7444 1.99 1.61 20.81 DW 5 1.77 21.159 Japan 0.1604 2 1.4251 2.3906 R 2 5 0.979 0.2584 2.73 21.13 1.90 DW 5 1.950 23.362 b South Africa 0.0085 2 1.1353 2.1390 R 2 5 0.973 0.1409 0.585 21.16 2.16 DW 5 1.741 23.895 a U.K. 0.0022 0.9973 0.0048 R 2 5 0.999 0.8064 2.67 198.22 0.99 DW 5 0.544 20.878 Implies significance at the 1 level. Implies significance at the 5 level. Implies significance at the 10 level. a Implies rejection of the null d 5 1 at the 1 level. b Implies rejection of the null d 5 1 at the 5 level. c Implies rejection of the null d 5 1 at the 10 level. t -statistics are in parentheses. DW 5 Durbin-Watson statistics. Fractional cointegration critical values: 23.834 1, 22.860 5, 22.371 10. Source Sephton 1995. The coefficient on lagged spot rate a 3 is found to be positive in all cases but significant in five cases. The coefficient on the forward rate a 1 is negative in five cases but, among these negative coefficients, significant only in the case of Hong Kong. Longworth 1981 found similar results, i.e., negative coefficients on the forward rate and significant positive coefficients on the lagged spot rate. The null hypothesis Table 8 KPSS test of the residuals Lags Australia Canada France Germany H Kong Italy Japan S Africa U.K. 0.549 a 0.278 b 0.106 0.090 0.220 b 0.333 b 0.099 0.134 0.069 3 0.433 a 0.289 b 0.112 0.094 0.316 b 0.280 b 0.093 0.100 0.061 6 0.451 a 0.288 b 0.124 0.108 0.316 b 0.282 b 0.104 0.131 0.064 a Implies rejection of cointegration at the 1 level. b Implies rejection of cointegration at the 5 level. KPSS critical values: 0.3727 1, 0.2177 5, 0.1617 10. Source: Harris and Inder 1994. T. Choudhry International Review of Economics and Finance 8 1999 433–453 443 Table 9 Unbiased forward rate hypothesis test Null Hypotheses—F Statistics Country H : a 1 5 1 H : a , a 1 , a 3 5 0, 1, 0 Australia 4.649 4.924 Canada 7.675 3.137 France 0.319 5.231 Germany 0.186 3.939 Hong Kong 131.770 46.462 Italy 0.595 3.224 Japan 3.720 5.199 South Africa 4.723 1.719 U.K. 0.292 107.930 Implies rejection of the null at the 1 level. Implies rejection of the null at the 5 level. Implies rejection of the null at the 10 level. of a unit coefficient on the forward rate is accepted only in France, Germany, Italy and the United Kingdom Table 9. This result is quite different from the previous semi-strong efficiency test Table 6. The null unbiased hypothesis is only found to be true for South Africa Table 9. Thus, once again South African currency is the only currency that provides evidence supportive of the semi-strong efficiency. Table 10 provides a comparison between results presented in this article and results of other research articles that apply some form of cointegration procedure. 26 As the table indicates results presented are not identical in each article. Of course along with the estimation procedure the sample period and the data frequency are also not identical. Most results presented do provide some evidence of the forward rate effi- ciency. Lack of evidence is noted during the latest floating era. This article and the Corbae et al. 1992 article do help redeem the latest floating era.

4. Mean-reversion in forward premium