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Biometrika 2008 95(2):365-379; doi:10.1093/biomet/asn009
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© 2008 Biometrika Trust

Articles

Modelling multiple time series via common factors

Jiazhu Pan

Department of Statistics, and Modelling Science, University of Strathclyde, Livingstone Tower, Richmond Street, Glasgow G1 1XH, U.K. jiazhu{at}stams.strath.ac.uk

Qiwei Yao

Department of Statistics, The London School of Economics, and Political Science, Houghton Street, London, WC2A 2AE, U.K. q.yao{at}lse.ac.uk

Received for publication 1 September 2006. Revision received 1 September 2007.
  Abstract

We propose a new method for estimating common factors of multiple time series. One distinctive feature of the new approach is that it is applicable to some nonstationary time series. The unobservable, nonstationary factors are identified by expanding the white noise space step by step, thereby solving a high-dimensional optimization problem by several low-dimensional sub-problems. Asymptotic properties of the estimation are investigated. The proposed methodology is illustrated with both simulated and real datasets.

Key Words: Cross-correlation function • Dimension reduction • Factor model • Multivariate time series • Non-stationarity • Portmanteau test • White noise


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