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Generalized canonical analysis for time series

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  • Robinson, P. M.

Abstract

Canonical correlation analysis is shown to be equivalent to the problem of estimating a linear regression matrix, B0, of less than full rank. After reparameterizing B0 some estimates of the new parameters, obtained by solving an eigenvalue problem and closely related to canonical correlations and vectors, are found to be consistent and efficient when the residuals are mutually independent. When the residuals are generated by an autocorrelated, stationary time series these estimates are still consistent and obey a central limit theorem, but they are no longer efficient. Alternative, more general estimates are suggested which are efficient in the presence of serial correlation. Asymptotic theory and iterative computational procedures for these estimates are given. A likelihoodratio test for the rank of B0 is seen to be an extension of a familiar test for canonical correlations.

Suggested Citation

  • Robinson, P. M., 1973. "Generalized canonical analysis for time series," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 141-160, June.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:2:p:141-160
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    Citations

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    Cited by:

    1. Zhou, Guofu, 1995. "Small sample rank tests with applications to asset pricing," Journal of Empirical Finance, Elsevier, vol. 2(1), pages 71-93, March.
    2. Burkett, John P., 1998. "Bureaucratic behavior modeled by reduced-rank regression: The case of expenditures from the Soviet state budget," Journal of Economic Behavior & Organization, Elsevier, vol. 34(1), pages 173-187, January.
    3. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    4. Bin Jiang & Anastasios Panagiotelis & George Athanasopoulos & Rob Hyndman & Farshid Vahid, 2016. "Bayesian Rank Selection in Multivariate Regression," Monash Econometrics and Business Statistics Working Papers 6/16, Monash University, Department of Econometrics and Business Statistics.
    5. Tayebi , Seyed Komail & Amini , Khaled Mohammad & Zamani , Zahra, 2012. "Inflation Determinants in Low and High Frequencies: An Implication of Spectral Analysis to Iran," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 7(1), pages 119-137, October.
    6. S. Yaser Samadi & L. Billard & M. R. Meshkani & A. Khodadadi, 2017. "Canonical correlation for principal components of time series," Computational Statistics, Springer, vol. 32(3), pages 1191-1212, September.

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