Can a simple structural time series model beat the random walk?

Abstract

This paper tries to address the question that if the long run PPP holds, then there should exist a structural model which can outperform the random walk in out of sample forecasting. We propose an ARFIMA based model with log of the independent variable as an explanatory variable and make a comparison study of this structural model with the benchmark random walk model. Then, we compare our results with that as obtained by Engel and Hamilton, and by Clarida, Sarno, Taylor and Valente. We present the standard ARFIMA model and show how can make an extension of it so that it becomes a variant of ARFIMA and name it as YQ-ARFIMA, then construct a bivariate model relating the dependent variable yt and ln yt , and with that, perform an impulse response function analysis of the predictive ability of ln yt . We also transform the YQ-ARFIMA into a moving average representation, and thereafter perform the impulse response function analysis again, then make a comparison study between the standard ARFIMA and the YQARFIMA by comparing the out of sample forecasting ability of each one of them with the benchmark random walk model. After that, compare the performance of YQ-ARFIMA with that of the Markov switching model put forward by Engel and Hamilton, and the MSIH(3)-VECM as put forward by CSTV. Last, we test the robustness of the YQ-ARFIMA by fitting it into different exchange rate series spanning the five continents of the globe, then, test the consistency of the forecast by YQ-ARFIMA by a cointegration technique. By using the loss functions RMSE and MAPE, cointegration consistency in forecasts and impulse response function analysis, we have shown beyond doubt that theYQ-ARFIMA model is very much superior in forecasting ability.