We propose a new diagnostic test for linear and nonlinear time series models,using a generalized spectral approach+ Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing“nuisance-parameter-free” property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic+ It is consistent against any type of pairwise serial dependence in the model standardized residuals and allows the choice of a proper lag order via data-driven methods. Moreover, the new test is asymptotically more efficient than the correlation integral?based test of Brock, Hsieh, and LeBaron (1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence) and Brock, Dechert, Scheinkman, and LeBaron (1996, Econometric Reviews 15, 197?235), the well-known BDS test, against a class of plausible local alternatives (not including ARCH). A simulation study compares the finite-sample performance of the proposed test and the tests of BDS, Box and Pierce (1970, Journal of the American Statistical Association 65, 1509?1527), Ljung and Box (1978, Biometrika 65, 297?303), McLeod and Li (1983, Journal of Time Series Analysis 4, 269?273), and Li and Mak (1994, Journal of Time Series Analysis 15, 627? 636). The new test has good power against a wide variety of stochastic and chaotic alternatives to the null models for conditional mean and conditional variance. It can play a valuable role in evaluating adequacy of linear and nonlinear time series models. An empirical application to the daily S&P 500 price index highlights the merits of our approach.

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 time-varying conditional volatility through a regime-switching GARCH model for both in-sample 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 Þnd that the models that provide good density forecast generally provide good forecast of Value-at-Risk.