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Biometrika 2006 93(2):399-409; doi:10.1093/biomet/93.2.399
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© 2006 Biometrika Trust

A test statistic for graphical modelling of multivariate time series

Yasumasa Matsuda

Faculty of Economics, Tohoku University, 27-1 Kawauchi, Aoba-ku, Sendai 980-8576, Japan. matsuda{at}econ.tohoku.ac.jp

A graphical model for multivariate time series is a concept extended by Dahlhaus (2000) from that for a random vector to a multivariate time series. We propose a test statistic for identifying the model based on the Kullback-Leibler divergence between two graphical models. The null distribution is shown to be asymptotically normal with mean and variance which depend just on the dimensions of the graphs.

Key Words: Asymptotic normality; Backward stepwise selection; Conditional independence; Graphical model; Kullback-Liebler divergence; Periodogram; Spectral density matrix; Test statistic.

Received January 2005. Revised November 2005.


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