Regularization for stationary multivariate time series

Yan Sun and Xiaodong Lin

Quantitative Finance, 2012, vol. 12, issue 4, 573-586

Abstract: The complexity of multivariate time series models increases dramatically when the number of component series increases. This is a phenomenon observed in both low- and high-frequency financial data analysis. In this paper, we develop a regularization framework for multivariate time series models based on the penalized likelihood method. We show that, under certain conditions, the regularized estimators are sparse-consistent and satisfy an asymptotic normality. This framework provides a theoretical foundation for addressing the curse of dimensionality in multivariate econometric models. We illustrate the utility of our method by developing a sparse version of the full-factor multivariate GARCH model. We successfully apply this model to simulated data as well as the minute returns of the Dow Jones industrial average component stocks.

Date: 2012
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DOI: 10.1080/14697688.2012.664933

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