On The Peña–Box Model

Abstract

Abstract. 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.