Model-free evaluation of directional predictability in foreign exchange markets, страница 20

c.

In summary, the GCS tests M_ZY1,0 and M_ZID1,0 show that the directions of the individual returns in spot and futures foreign exchange markets with any threshold are predictable using past history of both returns and interest rate differentials. Moreover, this evidence is generally stronger for greater movements c D 0.5,1. Our generalized cross-spectral derivative tests show that the level, volatility, skewness, kurtosis and direction of past returns and interest rate differentials are more or less useful in predicting the direction of individual currency returns. In particular, based on past returns, although the generally insignificant statistic M_ZY1,1 indicates a weak predictive power of conditional mean dynamics for the direction of future returns, we can see from M_ZY1,l for l D 2,3,4 and M_ZZ1,0 that strong dependencies derived from higher order conditional moments and the directions of past returns can attribute to the documented directional predictability. Furthermore, our GCS test results based on interest rate differentials suggest that the conditional mean dynamics of interest rate differentials contribute significantly to directional predictability, which provides an important policy implication—the monetary authorities can have substantial influence on the foreign exchange markets as they can affect the direction of future foreign exchange rates through the domestic (foreign) currency and/or the domestic interest rate. This monetary policy may be more effective with changes in the volatility of foreign exchange returns and/or the level of interest rate differentials.

5.2.  Directional Predictability of Joint Changes in Two Currencies

We now examine directional predictability of returns co-movements in foreign exchange rate markets. Specifically, we are interested in the direction of joint changes in two currencies within each spot market and each futures market.^[21] Consider individual returns fY_ktg,k D 1,2, where the subscript k denotes currency k. A new direction indicator of joint changes is then defined as follow:

                                         Z^C_t c,               c

                                          Z_t c,               c

for c_k D 0,0.5,1, in units of the sample standard deviation of fY_ktg, k D 1,2. As in the previous section, Z^C_t c and Z_t c can detect upward and downward market comovements, respectively. Further, with nonzero thresholds (i.e., c_k D 0.5,1), these indicators are able to detect greater co-movements between two currency returns.

In applying the GCS tests to directional predictability of joint changes, we use twofold tests: (i) a test of directional predictability using the past returns of two currencies, checking whether EZ_tj,Y EZ_t for all j > 0; (ii) a test of directional predictability using past individual returns of each currency, checking whether EZ_tEZ_t for all j > 0, and for k D 1,2. Naturally, the latter consists of two sets of GCS tests on the direction of changes in a single currency. Similar to Section 5.1, each of these GCS tests will be conducted with past currency returns and interest rate differentials.

We first report the GCS test results based on past returns in Table IV. For reasons of space, we only present the GCS test statistics for the direction of joint negative changes in the spot market. Overall, the patterns for the direction of joint positive changes are rather similar to those of joint negative changes, though less significant at times. Likewise, the results for the futures market are largely similar to those for the spot market, unless otherwise noted.²⁷

Table IV consists of three sections: the first section provides the GCS test statistics using past returns of two currencies jointly (hereafter denoted as ‘joint returns’), while the remaining

Table IV. GCS test statistics for negative joint changes in two currency spot rates (pD 21): using past returns