Markov switching in exchange rate models: will more regimes help?

Abstract

This paper examines the performance of Markov switching models of the exchange rate using a data-driven approach to determine the number of regimes rather than simply assuming two states. The analysis is conducted for the British pound, Canadian dollar, and Japanese yen exchange rates against the US dollar over the last 30 years with alternative specifications including a simple segmented trends model and Markov switching autoregressive models with monetary fundamentals. A noteworthy finding is that the number of regimes that minimizes mean square forecast errors tends to correspond to the number of regimes selected by Bayesian information criteria (but not Markov-switching-specific information criteria). For the monetary models, the number of regimes that minimizes forecast errors also tends to correspond to the most parsimonious model with well-behaved residuals. Although allowing for more regimes yields forecasting improvement over single- or two-regime models, the Markov switching model is still unable to outperform a random walk. This suggests that exchange rate models need to allow for novel, as opposed to repetitive or predetermined, structural change.

Appendix: out-of-sample testing procedure

This study evaluates the out-of-sample fit of the model following the tradition of Meese and Rogoff (1983). This method compares the predictive accuracy of the structural economic model to that of a simple random walk, using mean square error. In the tradition of Meese and Rogoff, this is a prediction exercise rather than forecasting because the actual values of the future X’s (regressors) are used to generate the out-of-sample predictions as opposed to requiring these to be forecasted as well.

Predictions are made by estimating the model up to time t, which generates initial coefficient estimates for the model. These estimates are combined with the actual values of the X’s at time $t+k$, where k is the forecast horizon. Predictions are generated for the 1-month horizon. Then t is moved forward by one period and the model is re-estimated and new predictions are generated.

The random walk predictions are generated very simply. It assumes that the best prediction of the exchange rate for any point in the future is given by today’s exchange rate. In terms of this out-of-sample exercise, this implies that the random walk prediction made at time t for $t+k$ is given by $s_t$, for $\hbox {k} = 1$.

From these predictions, forecast error statistics are calculated for both the economic model and the random walk model. In this paper, we evaluate the predicative ability of the model using mean square error statistic (MSE). Statistical significance of the difference between the MSE of the economic model and that of the random walk is estimated using the Diebold–Mariano 1995 test statistic.