Biometrika Advance Access originally published online on March 28, 2009
Biometrika 2009 96(2):494-496; doi:10.1093/biomet/asp009
Miscellanea |
Dimension reduction in time series and the dynamic factor model
Departamento de Estadística, Universidad Carlos III de Madrid, c/Madrid 126, 28903 Getafe, Spain daniel.pena{at}uc3m.es
Received for publication 1 September 2008. Revision received 1 October 2008.
This note shows that the dimension reduction method proposed by Li & Shedden (2002) is equivalent to the dynamic factor model introduced by Peña & Box (1987).
Key Words: Common factor Covariance matrix Dynamic principal component Reduced rank
References
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Ahn S. K. Inference of vector autoregressive models with cointegration and scalar components. J. Am. Statist. Assoc. (1997) 92:350–56.[CrossRef][Web of Science]
Ahn S. K., Reinsel G. C. Estimation for partially nonstationary multivariate autoregressive models. J. Am. Statist. Assoc. (1990) 85:813–23.[CrossRef][Web of Science]
Box G., Tiao G. A canonical analysis of multiple time series. Biometrika (1977) 64:355–65.
Forni M., Hallin M., Lippi M., Reichlein L. The generalized dynamic factor model: identification and estimation. Rev. Econ. Statist. (2000) 82:540–54.[CrossRef][Web of Science]
Hu Y., Chou R. On the Peña–Box model. J. Time Ser. Anal. (2004) 25:811–30.[CrossRef]
Hyvärinen A., Karhunen J., Oja E. M. Independent Component Analysis (2001) New York: John Wiley.
Li K. C., Shedden K. Identification of shared components in large ensembles of time series using dimension reduction. J. Am. Statist. Assoc. (2002) 97:759–65.[CrossRef][Web of Science]
Peña D., Box G. Identifying a simplifying structure in time series. J. Am. Statist. Assoc. (1987) 82:836–43.[CrossRef][Web of Science]
Peña D., Poncela P. Dimension reduction in multivariate time series. Advances on Distribution Theory, Order Statistics and Inference, in Honor of B. C. Arnold—Balakrishnan N., Castillo E., Sarabia J. M., eds. (2006a) Boston: Birkhauser.
Peña D., Poncela P. Nonstationary dynamic factor analysis. J. Statist. Plan. Infer. (2006b) 136:1237–57.[CrossRef]
Reinsel G. C., Velu R. P. Multivariate Reduced-Rank Regression (1998) New York: Springer.
Stock J. H., Watson M. W. Testing for common trends. J. Am. Statist. Assoc. (1988) 83:1097–107.[CrossRef][Web of Science]
Tiao G. C., Tsay R. S. Model specification in multivariate time series. J. R. Statist. Soc. B (1989) 51:157–213.
Velu R. P., Reinsel G. C., Wichern D. W. Reduced rank models for multiple time series. Biometrika (1986) 73:105–18.
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