Gaussian Approximation for High Dimensional Time Series

2015/08/27 by Danna Zhang, Zhang, Danna, Wei Biao Wu +1 · 7 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1508.07036

openalex publication_date 2015/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size n, the dimension p, the moment condition and the dependence of the underlying processes. We also consider an estimator for long-run covariance matrices and study its convergence properties. Our results allow constructing simultaneous confidence intervals for mean vectors of high-dimensional time series with asymptotically correct coverage probabilities. A Gaussian multiplier bootstrap method is proposed. A simulation study indicates the quality of Gaussian approximation with different n, p under different moment and dependence conditions.

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