On The Peña–Box Model

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Peña and Box [Journal of Americal Statistical Association (1987) Vol. 82, PP. 836–843] proposed a factor model which aimed to explore the possibility of using lower-dimensional series to represent or explain an observed higher-dimensional multiple time series. However, there were no statistics with distribution results with which to build the model. In this paper, we derive a statistical procedure to build the model for stationary and first-order non-stationary series. The main idea, conducted by the canonical correlation analysis between present series and non-present series, is an extension of the concept of the scalar component model proposed by Tiao and Tsay [Journal of the Royal Statistical Society B (1989) Vol. 51, pp. 157–213]. Finally, simulation studies and reanalysis of two real data sets are illustrated.

Keywords: Canonical correlation analysis; factor model; multiple time series

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9892.2004.00381.x

Affiliations: 1: National Chi Nan University 2: National Tsing Hua University

Publication date: November 1, 2004

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