A Simple Nearly Unbiased Estimator of Cross-Covariances

Journal of Time Series Analysis (Forthcoming).

32 Pages Posted: 1 Dec 2020

See all articles by Yifan Li

Yifan Li

Lancaster University - Department of Accounting and Finance; University of Manchester - Alliance Manchester Business School

Yao Rao

The University of Liverpool

Date Written: October 16, 2020

Abstract

In this paper, we propose a simple estimator of cross-covariance matrices for a multivariate time series with an unknown mean based on a linear combination of the circular sample cross-covariance estimator. Our estimator is exactly unbiased when the data generating process follows a Vector Moving Average (VMA) model with an order less than one half of the sampling period, and is nearly unbiased if such VMA model can approximate the data generating process well. In addition, our estimator is shown to be asymptotically equivalent to the conventional sample cross-covariance estimator. Via simulation, we show that the proposed estimator can to a large extent eliminate the finite sample bias of cross-covariance estimates, while not necessarily increase the mean squared error.

Keywords: cross-covariance, bias, multivariate time series.

Suggested Citation

Li, Yifan and Li, Yifan and Rao, Yao, A Simple Nearly Unbiased Estimator of Cross-Covariances (October 16, 2020). Journal of Time Series Analysis (Forthcoming)., Available at SSRN: https://ssrn.com/abstract=3713728

Yifan Li (Contact Author)

Lancaster University - Department of Accounting and Finance ( email )

The Management School
Lancaster LA1 4YX
United Kingdom

University of Manchester - Alliance Manchester Business School ( email )

Booth Street West
Manchester, M15 6PB
United Kingdom

Yao Rao

The University of Liverpool ( email )

Chatham Street
The University of Liverpool
Liverpool, L69 7ZH
United Kingdom

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