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Canonical correlation analysis for the vector AR(1) model with ARCH innovations
Authors:Ruey S. Tsay  Shiqing Ling
Affiliation:1. Graduate School of Business, University of Chicago, 5807 S. Woodlawn Avenue, Chicago, IL 60637, USA;2. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
Abstract:This paper extends the results of canonical correlation analysis of Anderson [2002. Canonical correlation analysis and reduced-rank regression in autoregressive models. Ann. Statist. 30, 1134–1154] to a vector AR(1) process with a vector ARCH(1) innovations. We obtain the limiting distributions of the sample matrices, the canonical correlations and the canonical vectors of the process. The extension is important because many time series in economics and finance exhibit conditional heteroscedasticity. We also use simulation to demonstrate the effects of ARCH innovations on the canonical correlation analysis in finite sample. Both the limiting distributions and simulation results show that overlooking the ARCH effects in canonical correlation analysis can easily lead to erroneous inference.
Keywords:62H10   62M10
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