Model-free evaluation of directional predictability in foreign exchange markets, страница 26

Notes:

1.  Cc1, currency 1; Cc2, currency 2.

2.  GCS tests are asymptotically one-sided N(0,1) tests and thus upper-tailed asymptotic critical values may also be used, which are 1.65 and 2.33 at the 5% and 1% levels, respectively. M(1,l) represents test statistics on the martingale test, serial correlation test, ARCH-in-mean test, skewness-in-mean test and kurtosis-in-mean test for l D 0,...4, respectively.

3.  The direction of joint negative changes is defined by Z_t c, where return of currency k is Y_kt D 100lnS_kt/S_kt1 for k D 1,2. Interest rate differential is defined by r_t  r_t^Ł where r_t is the domestic (US) risk-free interest rate and r_t^Ł is the foreign risk-free interest rate.

4.  A preliminary bandwidth p is crucial to run GCS tests. We have computed GCS test statistics for p D 11,...,50, but reported only for the value of p D 21 to save space.

changes of an economic time series is predictable using the past history of its own changes, and it further provides a class of separate inference procedures to explore possible sources of directional predictability. We have examined directional predictability for both foreign exchange spot rates and futures prices in six major currencies using two widely used and readily available aspects of market information: the past history of foreign exchange returns and interest rate differentials. We have documented strong evidence that 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, where the latter suggests that interest rate differentials can be a useful predictor of the direction of future foreign exchange rates. This evidence becomes stronger when we consider the direction of larger changes. Our results based on the separate inference procedures further demonstrate that, despite the weak conditional mean dynamics of foreign exchange returns, directional predictability can be explained by strong dependencies derived from higher-order conditional moments such as the volatility, skewness and kurtosis of past own foreign exchange returns. It is also documented that the conditional mean dynamics of interest rate differentials contributes significantly to directional predictability of foreign exchange rates.

We also examine the co-movements between two foreign exchange rates, especially the comovements of large changes. There is strong evidence that the directions of joint changes are predictable using past foreign exchange returns and/or interest rate differentials. Several sources can explain this directional predictability of joint changes. Among them, the levels of joint currency returns and the volatilities of past individual returns are remarkably useful in predicting the directions of joint changes.

Our findings have important policy implications. For example, the sources of directional predictability would be of importance to the monetary authorities who look for effective instruments to manage foreign exchange markets. Furthermore, the sources of directional predictability of joint (large) changes can provide useful information for understanding the dynamic characteristics of directional movements in crisis and of (extreme) directional comovements, which are useful in improving proactive risk management. Given various sources of directional predictability, it would be interesting to see how they can be developed into feasible modeling. We leave this for future research.

ACKNOWLEDGEMENTS

The authors are grateful to Warren Bailey, Robert Jarrow, Jaesun Noh and Byung-Sam Yoo for helpful comments and references, and to the Cheung Kong Scholarship of the Chinese Ministry of Education and Xiamen University, and the National Science Foundation for financial support via NSF Grant SES-0111769. We thank Steven Durlauf (Co-editor) and an anonymous referee for many constructive suggestions. Any remaining errors are solely ours. Views and opinions expressed here are those of the authors and do not necessarily reflect those of the Canadian Imperial Bank of Commerce.