Model-free evaluation of directional predictability in foreign exchange markets, страница 17

test suggests that the past own directions are useful in predicting future directions of exchange rate changes. This might be due to directional clustering, implying that an autologistic model of direction indicators may have some predictive ability for future directions. Nevertheless, the significance of separate inference tests M_ZY1,l does not necessarily imply that a simple polynomial model inwill forecast the direction of exchange rate changes well, particularly in an out-of-sample context (see Hong and Lee, 2006, for an out-of-sample forecasting exercise for foreign exchange rates). A high-order polynomial model may not be robust to outliers in a time series context, and foreign exchange returns may have a more subtle nonlinear dynamics, although the powers of lagged variable Y_tj have predictable ability. For example, a significant directional dependence on Y²_tj may be due to a bilinear or nonlinear moving average-type structure. Obviously, a comprehensive investigation of modeling and forecasting the nonlinear dynamics in foreign exchange rates is needed, but this is beyond the scope of the present paper.

We now turn to examining whether directional predictability of individual currency returns can be explained by interest rate differentials. Table III reports the test statistics M_ZID1,l for l D 0,1,2,3,4 and M_ZZID1,0. The omnibus test M_ZID1,0 checks whether interest rate differentials can be used to forecast the directions of individual currency returns, and various derivative tests M_ZID1,l for l D 1,2,3,4 examine specific types of cross-dependence between Z_t and fID_tj^l,j > 0g. Finally, the M_ZZID 1,0 statistic checks whether EZ_tjZ_ID,t EZ_t for all j > 0; namely it checks whether the direction of past interest rate differentials can be used to predict the direction of future returns in foreign exchange markets. As indicated in M_ZID1,0, there exists strong evidence of directional predictability using interest rate differentials, except for the positive direction of FJY and the negative direction of JY. The M_ZID1,0 test also suggests that the directions of the returns with large thresholds c D 0.5,1 are much easier to predict than those with zero threshold using interest rate differentials, although the value of M_ZID1,0 is not monotonically increasing in threshold c. These results provide considerable empirical support for the idea that interest rate differentials are a useful predictor for the directions of future foreign exchange rate changes.

Next, M_ZID1,1 shows strong evidence that the direction of individual currency returns is predictable using the level of interest rate differentials. Interestingly, in many cases the descriptive pattern of the statistical significance in the M_ZID1,1 test closely resembles that in the M test. For example, the values of M_ZID1,0 and M_ZID1,1 for AD and FAD exhibit a \-shape function of c for the negative directions. On the other hand, those of FCD exhibit a [-shape function of c for positive directions, and are monotonically decreasing in threshold c for negative directions. Since this pattern similarity associated with M_ZID1,0 is not found for the remaining GCS tests, it appears that a deriving source for directional predictability using interest rate differentials may be the time-varying conditional mean of interest rate differentials. This is consistent with Lothian and Wu’s (2003) finding that the level of interest rate differentials plays an important role in explaining predictability of exchange rate movements. They point out that large interest rate differentials have much stronger forecasting power of foreign exchange rates than small interest rate differentials (see also Flood and Rose, 2002; Huisman et al., 1998).