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In this paper we show that the Markov switching model is a relevant statistical alternative to the classical martingale model for exchange rates. By extending the standard Markov switching model we decisively reject the martingale model. Moreover, the model generates autocorrelations and linear structures in line with what is observed in reality. Subsequently, we test whether this model can explain chartist profits. We find that the extended Markov switching model is able to explain the profitability of a simple MA-30 rule. Finally, we decompose the profitability of the MA-30 rule into a linear and nonlinear part. We find that, although the implied linear structure of the Markov model explains a substantial part of the profitability, part of the profits of the MA-30 rule can be attributed to the specific nonlinearities implicit in the Markov model.

The success of technical trading rules in, for instance, the foreign exchange market constitutes a major puzzle in international finance.1 Not only does it create an anomaly with respect to the efficient market hypothesis (satisfactory explanations based on risk premia do not (yet) exist)2, it also raises questions about a more appropriate statistical and/or economic model for exchange rate returns than the standard martingale model. In this respect, technical trading rules are not very informative since most of these trading rules are not derived from a mathematically well-defined statistical or economic model. Instead, these rules are often ad hoc, with unknown statistical properties and, even worse, cannot be put into simple Markov-time algorithms (Neftci, 1991).3 As a result, the statistical and/or economic sources (causes) of the profitability of technical trading rules are not clearly identified and isolated. The contribution of this paper is to present an explicit nonlinear statistical alternative to the martingale model that allows us to analyze the source of the profitability of technical trading rules in greater detail. The class of statistical models considered in this paper is that of the Markov switching models. A priori this class of models emerges as a natural candidate since it is akin to technical trading rules in two respects. First, these models allow for stochastic trends (‘long swings’) in the asset price. Second, the Markov model implies that, as the filtering procedure of Hamilton (1989) shows, the sequence of past exchange rates contains useful information for the identification of the current trend of the exchange rate. Both features are in the core of the beliefs of technical traders. Moreover, the Markov switching models, as shown in this paper, belong to the class of price-trend models, introduced by Taylor (1980). Many of the statistical properties, including the linear representation, are known and can be tested in a straightforward manner. An early test of the Markov switching model as a potential null model for explaining chartist profits can be found in LeBaron (1998). However, the standard Markov switching model fails to detect significant switches in the trend of the exchange rates. We argue in Section 2 that this failure of the Markov switching model could be due to the assumption of a single latent variable driving the dynamics (both in mean and variance) of exchange rate returns. We extend the Markov switching model so that regime identification for the mean and the variance dynamics is performed independently. Anticipating the results, we do find statistically significant trends of opposite signs in weekly exchange rates. The martingale model can thus be replaced by this nonlinear statistical alternative. This extended Markov switching model, moreover, passes several additional specification tests. First, it reproduces many of the observed linear characteristics of exchange rate returns: low autocorrelations, an ARMA(1,1) representation that is almost observationally equivalent to white noise and weak out-of-sample predictability. Second, for most of the exchange rates considered, the model replicates the profitability of moving average rules. An important issue is whether these technical trading rules can be superior to standard linear time series analysis. Typically, technical trading rules will only be superior to standard linear models if (i) the exchange rate returns contain important nonlinear structures and (ii) the trading rules are able to pick up these nonlinearties. Several authors have argued that standard linear structures (ARMA(1,1)) are sufficient to explain technical trading rules (for instance, Taylor, 1980 and LeBaron, 1992). An obvious implication of this claim is that the trading rules are redundant and could be replaced by simpler trading rules based on linear time series models (see also Taylor, 1992). Others, including most practitioners, claim that the trading rules capture some inherent nonlinearity in the exchange rate returns (Neely et al., 1997, Gencay, 1999 and Neftci, 1991), implying non-redundancy of trading rule indicators. We introduce a method to decompose the profitability of technical trading rules into a part that can and cannot be explained by standard linear structures. We find for the moving average rules that, although a substantial part of the profitability is explained by linear structures, the specific nonlinear structures, implicit in the Markov switching model, explain an additional 10 to 15 percent of the profitability of moving average rules. These results, therefore, are more in line with the findings of Neftci (1991) and Neely et al. (1997) and point to the fact that trading rules do more than simply track the smooth (linear) trends in exchange rate returns. The remainder of the paper is organized in three sections. Section 2 develops the extended version of the Markov switching model, discusses its relation to the class of price-trend models of Taylor (1980) and presents estimates and diagnostics for the four major US-dollar exchange rates. Section 3 proceeds by discussing the relation between the Markov switching model and the observed profitability. Finally, we conclude in Section 4 by briefly summarizing the main findings and discussing the broader implications of the Markov switching model in other fields of exchange rate economics.

This paper presented evidence against the martingale model for exchange rates. Unlike many other papers, we do not test versus unrestricted alternatives, but against the specific alternative of an extended Markov switching model. This model was chosen because of the fact that a priori it is close to the ideas of technical traders, who strongly believe in stochastic trends. We find convincing evidence against the martingale model and in favor of the Markov switching model. The Markov model could, in theory, explain about 5 to 10 percent of the exchange rate variability of the four major exchange rates (quoted versus the US dollar). In practice, however, forecastability turns out to be much lower ranging from zero to about 2 percent. While the extended Markov model and its linear projection do not perform very well in forecasting exchange rate changes, they turn out to be relatively reliable sign predictors. Each of these models outperforms the standard martingale model in both sign prediction and profitability. Also, the models did perform marginally better than the MA-30 trading rule. Moreover, using Monte Carlo simulations, we showed that the Markov model can replicate the observed profitability of the MA-30 trading rule. These results are, moreover, robust for various window sizes of the moving average. Although the evidence is somewhat weaker, one can also extend this conclusion to the linear ARMA(1,1) representation of the Markov model. This suggests that persistent stochastic trends account for a substantial part of the observed profitability. Nonlinear structures, cannot be left out, however, as they explain an additional 10 to 15 percent of the profitability of the MA-30 rule. The implications of the validity of the (extended) Markov switching model, however, are not confined to explaining profitability of technical trading rules. Two implications are worth mentioning. First, the estimates in this paper clearly show that high frequency exchange rates are characterized by `long swings'. The presence of these swings can fundamentally affect inferences concerning the risk premium in exchange rate returns and hence might affect econometric results based on imputed risk premia (see Evans and Lewis, 1995). These findings are especially relevant for the UIP-puzzle and warrant some additional research. Second, the finding of inert stochastic trends gives additional support to those models that incorporate learning behavior, heterogeneous agents or persistent but time varying risk premia.