In this study, we formally test for nonlinear dependence in four currency futures
contracts traded on the International Monetary Market of the Chicago Mercantile Exchange, since most prior research studies have reported that financial time series exhibit nonlinear behaviour. Four nonlinear testing procedures are used. Our initial findings provide evidence of nonlinear dependence for all currencies; namely the British Pound (BP) the Japanese Yen (JY), the German Mark (DM) and the Swiss Franc (SF), each quoted in US dollars per foreign currency unit. As the BDS test rejects the null hypothesis of i.i.d. while the third moment test fails to reject multiplicative dependence, this suggests that the nonlinearity occurs in the variance of the process.
Since our results show significant ARCH effects; i.e., that large and small changes in returns tend to be systematically clustered over time, the study employs the
specifications of conditional heteroscedasticity and finds that Bollerslev's GARCH
generalization ( 1986) of the ARCH process provides a parsimonious model that
represents the data satisfactorily. As a result, further related analyses conducted in the study make use of similar GARCH procedures throughout. Perhaps the most important point to emerge from our empirical analysis is the ability of the GARCH ( 1, 1) model to capture nonlinear dependence in all the series.
Following the procedures laid down by Lamoureux and Lastrapes ( 1990), we test for the 'mixtures of distributions' hypothesis in which the stochastic mixing variable is hypothesized to be the rate of information arrival. Our findings on the contemporaneous relationship between volume and returns are consistent with this hypothesis, indicating that currency futures pricing appears to be efficient. The study also considers the informational role of contemporaneous volume with respect to volatility, and our results in this context show that trading volume contains significant explanatory power over the conditional variance in the GARCH specifications of the returns series.
The important contribution of this analysis to current research literature is the confirmation that, for currency futures, trading volume can effectively explain the conditional variance. Indeed, the GARCH effects diminish in all cases examined and this finding supports that of Lamoureux and Lastrapes (1990) for the stock market.
Moreover, the present study overcnmes the problem of the high serial correlation of volume by replacing it with unexpected volume in the conditional variance, following the procedure of Bessembinder and Seguin (1993). Using uncorrelated volume surprises, a similar result of a positive contemporaneous relationship between volume and return volatility is obtained, albeit with a slightly lower level 9f significance.
However, the GARCH effects remain significant; i.e., they do not vanish.
Next, we show that lagged uncorrelated volume has a low explanatory power, which confirms the role of contemporaneous (unexpected) volume, there being none of the problems of simultaneity in the conditional variance equation that were found by Najang and Yung (I 991) in treasury bond futures. In addition, we report results for subperiods which are almost identical to those of the full period, indicating structural stability in the entire sample period.
Finally, our results reveal that in the case of the conditional variance equation, ARCH effects exist simultaneously with spillover effects from other currencies for the BP and the DM, but not for the SF or the JY. Also, while the BP and the SF are found to be the main exporters of volatility to other currency futures, there is no clear evidence that any currency futures contract imports volatility on a bilateral basis. However, our results show that the inclusion of a third and fourth contract in the conditional variance equation reduces the volatility spillover between the first and second contracts, leading to the conclusion that a common economic effect is responsible to some extent for volatility interactions.