Can the Random Walk Model Be Beaten in Out-of-Sample Density Forecasts: Evidence from Intraday Foreign Exchange Rates

34 Pages Posted: 3 Aug 2003

See all articles by Yongmiao Hong

Yongmiao Hong

Cornell University - Department of Economics

Haitao Li

University of Michigan - Stephen M. Ross School of Business; Cheung Kong Graduate School of Business; Cheung Kong Graduate School of Business

Feng Zhao

University of Texas at Dallas - Jindal School of Management

Abstract

Numerous studies have shown that the simple random walk model outperforms all structural and time series models in forecasting the conditional mean of exchange rate changes. However, in many important applications, such as risk management, forecasts of the probability distribution of exchange rate changes are often needed. In this paper, we develop a nonparametric portmanteau evaluation procedure for out-of-sample density forecast and provide a comprehensive empirical study on the out-of-sample performance of a wide variety of time series models in forecasting the intraday probability density of two major exchange rates - Euro/Dollar and Yen/Dollar. We find that some nonlinear time series models provide better density forecast than the simple random walk model, although they underperform in forecasting the conditional mean. For Euro/Dollar, it is important to model heavy tails through a Student-t innovation and asymmetric timevarying conditional volatility through a regime-switching GARCH model for both insample and out-of-sample performance; modeling conditional mean and serial dependence in higher order moments (e.g., conditional skewness), although important for in-sample performance, does not help out-of-sample density forecast. For Yen/Dollar, it is also important to model heavy tails and volatility clustering, and the best density forecast model is a RiskMetrics model with a Student-t innovation. As a simple application, we find that the models that provide good density forecast generally provide good forecast of Value-at-Risk.

Keywords: density forecasts, eurodollar, GARCH, intraday exchange rate, jumps, maximum likelihood estimation, nonlinear time series, out-of-sample forecasts, regime-switching

JEL Classification: C4, E4, G0

Suggested Citation

Hong, Yongmiao and Li, Haitao and Zhao, Feng, Can the Random Walk Model Be Beaten in Out-of-Sample Density Forecasts: Evidence from Intraday Foreign Exchange Rates. Available at SSRN: https://ssrn.com/abstract=424381 or http://dx.doi.org/10.2139/ssrn.424381

Yongmiao Hong (Contact Author)

Cornell University - Department of Economics ( email )

Department of Statistical Science
414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-5130 (Phone)
607-255-2818 (Fax)

Haitao Li

University of Michigan - Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States
734-615-5475 (Phone)

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Cheung Kong Graduate School of Business ( email )

Oriental Plaza, Tower E3
One East Chang An Avenue
Beijing, 100738
China

Feng Zhao

University of Texas at Dallas - Jindal School of Management ( email )

800 W. Campbell Rd. SM 31
Richardson, TX 75080
United States
972-883-5815 (Phone)

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