Model-free evaluation of directional predictability in foreign exchange markets, страница 8

Another way to view a rejection of the null in (4) is similar to what we have discussed previously for ₀ in (2). That is, it should be viewed as a necessary but not sufficient condition for the effectiveness of a successful interest rate defense.^[10] Given the rejection of the null hypothesis ₀ in (4), the monetary authorities may affect the direction of foreign exchange rates by raising/lowering domestic interest rates to discourage speculative currency attacks.¹¹ In this regard, successful interest rate defenses can be attributed to the existence of dependence between the direction of exchange rate changes and interest rate differentials. Further, within this context, a comparison between the effects of past returns and past interest rate differentials on the direction of foreign exchange returns gives valuable information about which instruments are a more effective tool for the monetary authorities to accomplish their objective. Thus the use of other market information I^ID_t1 can provide further insights on directional predictability of foreign exchange rates.

It is well known that there exist volatility co-movements (e.g., Hamao et al., 1990). Some authors (Longin and Solnik, 1995; Ramchand and Susmel, 1998) show that correlation between markets may increase during periods of high volatility. If the skewness varies jointly between two markets, this will suggest an increase in the probability of the occurrence of a large event with the same sign on both markets. If the kurtosis varies jointly between two markets, there will be an increase in the probability of the occurrence of a large event on the markets, whatever the direction of the shock is. Jondeau and Rockinger (2003) also show that there is evidence that large events generating skewness tend to occur simultaneously for stock markets. In other words, very large events of a given sign tend to occur jointly. In particular, this result indicates that crashes will tend to happen at the same time. Building on these backgrounds, it will be interesting to examine whether the direction of joint changes in two currencies, particularly the direction of large changes in two markets, is predictable using various moments of market information available.

3.  EVALUATION METHOD

As discussed earlier, the dynamics of directional predictability of asset returns is highly nonlinear due to the fact that directional predictability depends on serial dependence in every timevarying conditional moment. We thus use a nonlinear analytic tool, namely the generalized cross-spectrum approach primarily employed in Hong and Chung (2006). The generalized crossspectrum approach, which extends Hong’s (1999) univariate generalized spectrum to a bivariate time series context, is based on the spectrum of the transformed time series via the characteristic function, allowing us to detect both linear and nonlinear cross-dependencies. Formally, for a strictly stationary bivariate process fZ_t,Y_tg, whose marginal characteristic functions are Ee^iuZt and ϕ_Yu D Ee^iuYt, and whose pairwise joint characteristic function is ϕ_ZY,ju,

E[e^iuZ] for u, 1 and j D 0,š1,..., the generalized cross-spectrum is defined by

                                              f_ZYω,u, _ZY,ju,ve^ijω,                 ω    ,],                                    5

2 jD1

where ω is the frequency and _ZY,ju,v is the generalized cross-covariance function between the transformed series:

                                                                _ZY,ju, cove^iuZt,e.                                                              6

             It is easy to see that _ZY,ju,                        0 for all u, if and only if Z_t and Y