ABSTRACT
Up to now, we have largely assumed that the data we analyze by generalized structured component analysis consist of cases (subjects) by variables matrices, in which the cases can usually be assumed to be statistically independent. However, this is not always the case. In this chapter, we discuss an extension of generalized structured component analysis to analyzing time series data, which often arise from repeated measurements of a quantity or quantities over time. Time series data are temporally (serially) correlated. To account for the correlations, we incorporate multivariate autoregressive models into generalized structured component analysis. The proposed method is called dynamic generalized structured component analysis. The word “dynamic” here refers to a process in which a state of a variable at a particular time may be inuenced by a state of the same or other variables at previous times. The bootstrap procedure needs a special attention to deal with the temporal correlations. In this chapter, we treat time as a discrete variable. See Suk and Hwang (2014), and the next chapter (Chapter 11) for an extension of generalized structured component analysis, which treats the time variable as continuous. The method in Chapter 11 also treats time as an extension of variables (corresponding to the columns of a data matrix), whereas the approach in this chapter treats observed time points as an extension of cases (corresponding to the rows).
