Groupe d’études et de recherche en analyse des décisions

G-2005-66

On Testing for Serial Correlation with a Wavelet-Based Spectral Density Estimator in Multivariate Time Series

A new one-sided test for serial correlation in multivariate time series models is proposed. The test is based on a comparison between a multivariate spectral density estimator and the spectral density under the null hypothesis of no serial correlation. Duchesne and Roy (2004) considered a multivariate kernel-based spectral density estimator. However, when the spectral density exhibits irregular features (because of strong autocorrelation, seasonality, amongst others), it is expected that a multivariate wavelet-based spectral density estimator will capture more effectively the local behavior of the spectral density. We consider a test based on a wavelet spectral density estimator, which represents a generalization of a test proposed by Lee and Hong (2001). The asymptotic distribution of the new test is established under the null hypothesis, which is N(0, 1). We propose and justify a suitable data-driven method to choose the smoothing parameter of the wavelet estimator (called the finest scale in that context). The new test should be powerful when the spectral density contains peaks or bumps. This is confirmed in a simulation study, where kernel-based and wavelet-based estimators are compared.

, 50 pages