Model-free evaluation of directional predictability in foreign exchange markets, страница 15

Next, M_ZY1,3 and M_ZY1,4 display patterns similar to M_ZY1,2, and these similarities are much clearer for the statistic M_ZY1,4. There is generally consistent evidence that the direction of large returns c D 0.5,1 is predictable using past skewness and kurtosis. Greater directional predictability is found in the spot market than in the futures market. However, unlike M_ZY1,2, there seems no clear evidence that the direction of negative returns is easier to predict than that of positive returns using past skewness and kurtosis of individual currency returns.

Finally, like M_ZY1,0, the M_ZZ1,0 test indicates that the directions of future individual currency returns are predictable using the directions of past individual currency returns, and become more predictable with larger thresholds. It is also easier to predict the directions of the returns in spot rates than in futures prices with large thresholds (c D 0.5,1). The M_ZZ1,0 test further suggests that the direction of negative returns is easier to predict than that of positive returns, using the directions of past returns.

In light of the above results, nonlinear models can be more useful in predicting the foreign exchange dynamics than linear regression models. For example, the significance of the M_ZZ1,0

Table II. GCS test statistics for changes in single currency spot and futures (pD 21): using past returns