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.All matrices, C Z (h), h " 0, are of rank r, the number of factors, and have the same null space. Hence, a (k À r) · k matrix, M 1 , exists such thatThis reminds us of the SCM(0,0), a special case of the SCM proposed by Tiao and Tsay (1989). In that paper, Z t is said to have (k À r) SCM(0,0) if a 812

As a response to the growing concern on the interconnection of international stock markets, this study uses the Pena-Box model to capture time-varying relationship of the returns of 13 stock indices during 1993-2002. The results indicate a dynamic relationship of world major stock markets over time, which provide new but supplemental evidence on the conclusion derived from the conventional confirmatory factor analyses in literature.

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