A note on testing for homoscedasticity in high-dimensional time series

Abstract

We consider the problem of testing for homoscedasticity in high-dimensional time series, under the assumption that the sample size n and the dimension p satisfy [Formula: see text] as [Formula: see text]. The homoscedasticity refers to the case where the covariance matrix of the time series is equal to the identity. The test statistic is so-called the V-statistic in the multivariate statistics. The asymptotic null distribution of the V-statistic is shown to be asymptotically normal. The simulation study illustrates the finite sample properties of the V-statistic.

Keywords

• Asymptotic theory
• high dimensional time series
• homoscedasticity
• V-statistic