2.1 Dynamic principal component analysis (DPCA)

In dynamic PCA, first proposed by Ku et al. [4], the PCA model is built on the data matrix X residing in the window, to account for auto- and crosscorrrelation between variables. This approach implicitly estimates the autoregressive structure of the data (e.g., [5]). As functions of the model, the T<sup>2</sup> and Q-statistics will also be functions of the lag parameters. Since the mean and covariance structures are assumed to be invariant, the same global model is used to evaluate observations at any future time point.

Although dynamic PCA is designed to deal with autocorrelation in the data, the resultant score variables will still be autocorrelated or even crosscorrelated when no autocorrelation is present [4, 6]. These autocorrelated score variables have the drawback that they can lead to higher rates of false alarms when using Hotelling's T<sup>2</sup> statistic.

Several remedies have been proposed to alleviate this problem, for example, wavelet filtering [7], ARMA filtering [6], and the use of residuals from predictive models [8]. Nonlinear PCA models have been considered by several authors [9–13].
