Asymptotic Theory of Test Statistic for Sphericity of High-Dimensional Time Series

Yan Liu, Yurie Tamura, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    Abstract

    We consider the testing problem for the sphericity hypothesis regarding the covariance matrix based on high-dimensional time series, under the assumption that the sample size n and the dimension p satisfy Limn,p→∞ p/n = c ∈ (0, ∞). Recently, several studies on test statistics for sphericity of independent and identically distributed p-dimensional random variables have been carried out under the assumption that both n and p diverge to infinity. A test statistic for sphericity has been proved to be well behaved even when p>n. We investigate the test statistic under situations of high-dimensional time series. The asymptotic null distribution of the test statistic is shown to be standard normal distribution when the observations come from Gaussian stationary processes. In the simulation study, we illustrate the properties of the test statistic for several time series models. We apply the test to a problem of portfolio selection in our empirical study.

    Original languageEnglish
    Pages (from-to)402-416
    Number of pages15
    JournalJournal of Time Series Analysis
    Volume39
    Issue number3
    DOIs
    Publication statusPublished - 2018 May 1

    Fingerprint

    Sphericity
    Asymptotic Theory
    Test Statistic
    Time series
    High-dimensional
    Statistics
    Standard Normal distribution
    Stationary Gaussian Process
    Portfolio Selection
    Null Distribution
    Time Series Models
    Normal distribution
    Covariance matrix
    Diverge
    Random variables
    Identically distributed
    Empirical Study
    Asymptotic distribution
    Sample Size
    Random variable

    Keywords

    • Asymptotic theory
    • high dimensional time series
    • sphericity test

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty
    • Applied Mathematics

    Cite this

    Asymptotic Theory of Test Statistic for Sphericity of High-Dimensional Time Series. / Liu, Yan; Tamura, Yurie; Taniguchi, Masanobu.

    In: Journal of Time Series Analysis, Vol. 39, No. 3, 01.05.2018, p. 402-416.

    Research output: Contribution to journalArticle

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