Department of Economics and Business Economics

A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

Research output: Working paper/Preprint Working paperResearch

Standard

A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. / Proietti, Tommaso; Giovannelli, Alessandro.

Aarhus : Institut for Økonomi, Aarhus Universitet, 2017.

Research output: Working paper/Preprint Working paperResearch

Harvard

Proietti, T & Giovannelli, A 2017 'A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices' Institut for Økonomi, Aarhus Universitet, Aarhus.

APA

Proietti, T., & Giovannelli, A. (2017). A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. Institut for Økonomi, Aarhus Universitet. CREATES Research Papers No. 2017-20

CBE

Proietti T, Giovannelli A. 2017. A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. Aarhus: Institut for Økonomi, Aarhus Universitet.

MLA

Proietti, Tommaso and Alessandro Giovannelli A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. Aarhus: Institut for Økonomi, Aarhus Universitet. (CREATES Research Papers; Journal number 2017-20). 2017., 23 p.

Vancouver

Proietti T, Giovannelli A. A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. Aarhus: Institut for Økonomi, Aarhus Universitet. 2017 May 17.

Author

Proietti, Tommaso ; Giovannelli, Alessandro. / A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices. Aarhus : Institut for Økonomi, Aarhus Universitet, 2017. (CREATES Research Papers; No. 2017-20).

Bibtex

@techreport{02f6f918e66e445088469880485416ce,
title = "A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices",
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.",
keywords = "Toeplitz systems, Optimal linear prediction, Partial autocorrelation function",
author = "Tommaso Proietti and Alessandro Giovannelli",
year = "2017",
month = may,
day = "17",
language = "English",
series = "CREATES Research Papers",
publisher = "Institut for {\O}konomi, Aarhus Universitet",
number = "2017-20",
type = "WorkingPaper",
institution = "Institut for {\O}konomi, Aarhus Universitet",

}

RIS

TY - UNPB

T1 - A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

AU - Proietti, Tommaso

AU - Giovannelli, Alessandro

PY - 2017/5/17

Y1 - 2017/5/17

N2 - 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.

AB - 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.

KW - Toeplitz systems, Optimal linear prediction, Partial autocorrelation function

M3 - Working paper

T3 - CREATES Research Papers

BT - A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices

PB - Institut for Økonomi, Aarhus Universitet

CY - Aarhus

ER -