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Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices

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  • Steland, Ansgar

Abstract

This paper studies a flexible approach to analyze high-dimensional nonlinear time series of unconstrained dimension based on linear statistics calculated from spectral average statistics of bilinear forms and nonlinear transformations of lag-window (i.e. band-regularized) spectral density matrix estimators. That class of statistics includes, among others, smoothed periodograms, nonlinear statistics such as coherency, long-run-variance estimators and contrast statistics related to factorial effects as special cases. Especially, we introduce the class of nonlinear spectral averages of the spectral density matrix. Having in mind big data settings, we study a sampling design which includes a sparse sampling scheme. Gaussian approximations with optimal rate are derived for nonlinear time series of growing dimension for these frequency domain statistics and the underlying lag-window (cross-) spectral estimator under non-stationarity. For change-testing (self-standardized) CUSUM statistics are examined. Further, a specific wild bootstrap procedure is proposed to estimate critical values. Simulation studies and an application to SP500 financial returns are provided in a supplement to this paper.

Suggested Citation

  • Steland, Ansgar, 2024. "Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:jmvana:v:199:y:2024:i:c:s0047259x2300091x
    DOI: 10.1016/j.jmva.2023.105245
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    References listed on IDEAS

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    7. Shao, Xiaofeng, 2010. "The Dependent Wild Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 218-235.
    8. Steland, Ansgar, 2020. "Testing and estimating change-points in the covariance matrix of a high-dimensional time series," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    9. Monika Bours & Ansgar Steland, 2021. "Large‐sample approximations and change testing for high‐dimensional covariance matrices of multivariate linear time series and factor models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 610-654, June.
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