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Consistent autoregressive spectral estimates: Nonlinear time series and large autocovariance matrices

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  • Jiang Wang
  • Dimitris N. Politis

Abstract

We consider the problem of using an autoregressive (AR) approximation to estimate the spectral density function and the n × n autocovariance matrix based on stationary data X1, … , Xn. The consistency of the autoregressive spectral density estimator has been proven since the 1970s under a linearity assumption. We extend these ideas to the nonlinear setting, and give an application to estimating the n × n autocovariance matrix. Under mild assumptions on the underlying dependence structure and the order p of the fitted AR(p) model, we are able to show that the autoregressive spectral estimate and the associated AR‐based autocovariance matrix estimator are consistent. We are also able to establish an explicit bound on the rate of convergence of the proposed estimators.

Suggested Citation

  • Jiang Wang & Dimitris N. Politis, 2021. "Consistent autoregressive spectral estimates: Nonlinear time series and large autocovariance matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 580-596, September.
    • Handle: RePEc:bla:jtsera:v:42:y:2021:i:5-6:p:580-596
    DOI: 10.1111/jtsa.12580
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    References listed on IDEAS

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    1. Timothy L. McMurry & Dimitris N. Politis, 2010. "Banded and tapered estimates for autocovariance matrices and the linear process bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 471-482, November.
    2. McMurry, Timothy L & Politis, D N, 2010. "Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap," University of California at San Diego, Economics Working Paper Series qt5h9259mb, Department of Economics, UC San Diego.
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    Cited by:

    1. Matei Demetrescu & Mehdi Hosseinkouchack, 2022. "Autoregressive spectral estimates under ignored changes in the mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 329-340, March.

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