Fundamental structural changes over time and predictability of exchange rates: a Monte Carlo study of time varying regression and applications

The difficulties of modeling and forecasting foreign exchange rates have been well known since early 1970's. One of the possible explanations for our inability to provide an accurate model is the structural changes over time, especially in emerging markets. The traditional regression techniques that assume constant parameters are incapable of capturing the changing dynamics over time. Consequently, most foreign exchange regression models are ineffective.

To better capture fundamental structural changes in a market, a moving block regression technique is recommended by the author. The moving block regression procedure utilizes sub-sample information, rather than the prevailing whole sample data that intends to increase regression efficiency with more observations. To find out the loss or gain of forecast efficiency, a Monte Carlo study is carried out under several different scenarios: data in compliance with the classic OLS assumptions, data with heteroscedasticity, data with autocorrelation, model with a missing variable, model with changing regression coefficients, and data with nonlinear relationships.

Simulation results show a trivial loss of out-of-sample forecast efficiency with the moving block regressions and a small trade-off in the presence of minor violations of the assumptions. However, there is a clear dominance of the moving block regressions over the traditional whole sample regressions in terms of forecasting efficiency when the violations of assumptions are serious, such as missing variable, changing coefficients, or nonlinear relations.

Then the moving block regressions are applied to exchange rates of six currencies against the U.S. dollar. The comparisons of forecasting residuals, both in-sample and out-of-sample, show a strong support for the moving block techniques, indicating the inevitable violations of regression assumptions in foreign exchange markets.