Estimation of the Generalized Prediction Error Variance of a Multiple Time Series

原文摘要

For a multivariate stationary time series, we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the Szegö-Kolmogorov formula, replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator. Asymptotic normality of this estimator is established, and its small-sample behavior is assessed through simulation and application to two real data sets. These examples show that the proposed method works reasonably well in comparison with parametric models. In contrast to the univariate case where smoothing the periodogram is optional and generally not recommended, in the multivariate case this smoothing is a necessity, because the raw periodogram is a matrix of rank one. To obtain a consistent estimator of a full-rank spectral density matrix, one must necessarily choose larger bandwidths for higher-dimensional time series. A bias-correction factor is computed using the asymptotic properties of our proposed estimator, and a simulation study indicates its important role in reducing the bias.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）