Can the Random Walk Model be Beaten in Out-Of-Sample Density Forecasts? Evidence from...

Yongmiao Hong, Haitao Li, Feng Zhao

Journal of Econometrics 141 (2007) 736–776

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It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance.We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regimeswitching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.

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Keywords: Density forecasts; GARCH; Intraday exchange rate; Jumps; Maximum likelihood estimation;Nonlinear time series; Out-of-sample forecasts; Regime-switching