Canonical correlation analysis for the vector AR(1) model with ARCH innovations
- 作者：Ruey S. Tsay ; Shiqing Ling
- 关键词：Canonical correlations and vectors ; Eigenvalues and eigenvectors ; Asymptotic distribution ; Conditional heteroscedasticity
- 刊名：Journal of Statistical Planning and Inference
- 出版年：2008
- 期刊代码：36_03783758
- 类别：mt
- 出版时间：1 September 2008
- 卷：138
- 期：9
- 页码：2826-2836
- 文件大小：365 K
摘要
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.