Model-free evaluation of directional predictability in foreign exchange markets, страница 5

It is important to consider directional predictability of the foreign exchange rate with different threshold values for the following reasons. First, since an asset price may be quoted in minimum price increments (or ticks), marginal investors who determine market prices may be more interested in whether the asset prices rise above or fall below such thresholds. In a similar vein, those investors who are in pursuit of profit may be further interested in the direction of the changes large enough to ensure net profits after transaction costs. Therefore, the provision of a threshold value can be seen as representing practical considerations to help build more successful trading strategies. Next, the deriving forces of small and large changes in asset prices may be different. Maheu and McCurdy (2003), for example, show that the dynamics of returns can consist of two different components: (i) occasional jumps (i.e., large changes),^[4] which are driven by important news events, and tend to be clustered together; (ii) (smooth) small changes, which are due to liquidity trading or strategic trading, as information dissimilates over time. At the same time, it has been observed that there is an asymmetry in the dependence structure for small and large changes, as in Longin and Solnik (2001), Ang and Chen (2002), and Hong et al. (2007), who found the correlation is stronger between large changes than that between small changes, and even stronger on the downside (i.e., negative large returns). Lastly, investors may have different valuation assessments between small and large changes in the foreign exchange rates. For example, momentum traders, who seek to exploit a short-term trend, may react more strongly to large changes since the direction and strength of the trend become more recognizable at the larger changes. In addition, large changes often contain more valuable information, while small changes display mere noise. Therefore, it is necessary for investors to segment price changes so as to filter out irrelevant information from the observations.^[5]

In practice, the choice of threshold c can either be made conditional on data or held fixed at multiple values such as tick sizes or transaction costs. There is no obvious rationale for preferring one or another criterion: a posterior threshold gained from the observations may be more suitable for the purpose of statistical data analysis, while the latter will be of interest to those in pursuit of practical use. Since our study concerns a statistical evaluation of directional predictability, we_p

will use the multiples of the standard deviation _Y D                  varY_t without loss of generality.^[6]

We are interested in testing whether the direction of foreign exchange rate changes with threshold c is predictable using the history of its own past changes. The null hypothesis is

                                                     ₀ :E[Z_tc[Z_tc] almost surely a.s.                                                2

where I_t is the information set available at time t  1. Note that our null hypothesis ₀ is not the same as the hypothesis of EY a.s. for some constant , where the latter hypothesis checks whether there exists a predictable time-varying conditional mean. It is shown that, irrespective of the existence of a time-varying conditional mean predictability, directional predictability may exist through the interaction between a nonzero unconditional mean , volatility dependence, and serial dependence in higher-order conditional moments such as skewness and kurtosis (Christoffersen and Diebold, 2002; Hong and Chung, 2006). This fact, that directional predictability can be derived from such various sources, may explain why it is easier to predict the direction than the level of the change, as many empirical studies document.