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A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

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Abstract
We consider the problem of estimating the high-dimensional autocovariance matrix of a stationary random process, with the purpose of out of sample prediction and feature extraction. This problem has received several solutions. In the nonparametric framework, the literature has concentrated on banding and tapering the sample autocovariance matrix. This paper proposes and evaluates an alternative approach, based on regularizing the sample partial autocorrelation function, via a modified Durbin-Levinson algorithm that receives as input the banded and tapered partial autocorrelations and returns a sample autocovariance sequence which is positive definite. We show that the regularized estimator of the autocovariance matrix is consistent and its convergence rates is established. We then focus on constructing the optimal linear predictor and we assess its properties. The computational complexity of the estimator is of the order of the square of the banding parameter, which renders our method scalable for high-dimensional time series. The performance of the autocovariance estimator and the corresponding linear predictor is evaluated by simulation and empirical applications.

Suggested Citation

  • Tommaso Proietti & Alessandro Giovannelli, 2017. "A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices," CEIS Research Paper 410, Tor Vergata University, CEIS, revised 19 Jul 2017.
    • Handle: RePEc:rtv:ceisrp:410
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    References listed on IDEAS

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    11. Datta Gupta, Syamantak & Mazumdar, Ravi R. & Glynn, Peter, 2013. "On the convergence of the spectrum of finite order approximations of stationary time series," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 1-21.
    12. 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:

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    2. Serge B. Provost & John N. Haddad, 2019. "A recursive approach for determining matrix inverses as applied to causal time series processes," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 53-62, April.

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    More about this item

    Keywords

    Toeplitz systems; Optimal linear prediction; Partial autocorrelation function;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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