Lee, Tae-Hwy: Inference and Forecast of Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models
World Conference Econometric Society, 2000, Seattle

Yongmiao Hong, Cornell University
Tae-Hwy Lee, University of California, Riverside
Inference and Forecast of Exchange Rates via Generalized Spectrum and Nonlinear Time Series Models
Session: C-11-17  Tuesday 15 August 2000  by Lee, Tae-Hwy
It is often documented, based on autocorrelation, variance ratio and power spectrum, that exchange rates approximately follow a martingale process. Because autocorrelation, variance ratio and spectrum essentially check serial uncorrelatedness rather than martingale difference, they may deliver misleading conclusions in favor of the martingale hypothesis when the test statistics are insignificant. In this paper we explore whether there exists a gap between serial uncorrelatedness and martingale difference for exchange rate changes, and if so, whether nonlinear time series models admissible in the gap can outperform the martingale model in forecasting. Using the generalized spectral density tests of Hong (1999), we find that there exists strong nonlinear dependent (although often linearly uncorrelated) structure in the conditional mean of the changes of five major exchange rates considered, in addition to the well-known volatility clustering. To model the nonlinearity in conditional mean, we consider, among other things, the functional-coefficient (FC) model of Cai, Fan, and Yao (1998) where the coefficients are time-varying and state-dependent. The state-dependence is governed with moving average technical trading rules (MATR) so that the model parameters depend on the investment positions implied by the trading rules. Out-of-sample forecast performances of a variety of nonlinear models are compared with a benchmark martingale model, and are evaluated using the criteria of trading returns and directional forecasts via White's (1998) reality check method, which accounts for model dependence and thus the biases due to data-snooping. It is found that some nonlinear models (FC and MATR) do have predictive ability for Japanese Yen, Canadian dollar, and French Franc, but not for Deutschemark and British pound.

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