Model-free evaluation of directional predictability in foreign exchange markets, страница 4

As pointed out earlier, the preceding studies described are model specific. They provide directional predictability of models (rather than data), but cannot explain why there exists such an opportunity to profit in the foreign exchange market from the currency attacks or technical trading rules. In contrast, our model-free evaluation will provide a statistical explanation based upon raw observed data about whether the direction of changes is predictable. In addition, it provides some guidance in constructing forecast models, such as the choice of information sets and conditional variables.

Based on a sample of spot rates and futures prices in six major currencies, our analysis reveals a number of interesting findings. First, we find significant evidence on directional predictability for the majority of both spot and future foreign exchange rates. The directions of foreign exchange returns can be predicted not only by the past history of foreign exchange returns, but also by the past history of interest rate differentials. Directional predictability for larger returns is stronger, owing to the persistent volatility clustering of past foreign exchange rate changes and the timevarying conditional mean dynamics of interest rate differentials. We also find significant evidence on directional predictability of the co-movement between two foreign exchange rates, especially the co-movement of large changes. These results are useful for financial risk management and investment diversification, as they provide useful information for understanding extreme market movements and extreme market co-movements.

Our findings have important implications. First, the evidence of directional predictability provides a solid statistical basis for any successful directional forecast models and technical trading rules. Second, our results suggest that interest rate differentials can be useful instruments in predicting the direction of foreign exchange rate changes. Third, the documented dependencies between the direction of foreign exchange rate changes and two conditioning series—the past exchange rate changes and past interest rate differentials—suggest that both foreign exchange market intervention and interest rate defense can be effective tools in managing foreign exchange markets. Lastly, our evidence of directional predictability of joint changes in two currencies suggests that it is possible to predict simultaneous foreign exchange markets movements.

The paper is organized as follows: Section 2 discusses hypotheses on directional predictability in foreign exchange rate changes, including those large changes and the direction of co-movements in two currencies. Section 3 describes the model-free evaluation methods for directional predictability. Section 4 describes the data and summary statistics, Section 5 presents our empirical findings and discusses their implications, and Section 6 contains concluding remarks and directions for future research.

2.  DIRECTIONAL PREDICTABILITY IN FOREIGN EXCHANGE MARKETS

Let Y_t denote the return of the spot foreign exchange rate S_t at time t. We define a direction indicator function

                                                                       Z_tc      > c                                                                     1

where  denotes the indicator function, taking value 1 when Y_t > c and value zero when Y_t  c, and c is a threshold constant. This indicator function characterizes the direction of positive price changes. A similar indicator function can be defined for the direction of negative price changes when Y_t .