Ewma charts for multivariate time series

Abstract

In this paper a muIt,ivariat.e EWMA chart for time series is introduced. In principle, it is a generalization of the control scheme of Lowry et al. (I992) for multivarite indendent observations. The autocovariances of the EWMA recursion are derived for stationary multivariate time series. IYsing tllese reslllts a co11t.rol chart hased or1 t11 illt.ivariate EWMA recursion is proposed. For a multivariate autoregressive process of order 1, a sufficient. condition is given such that the in-control average run length (ARL) is invariant, withrespect to the covariance of the White Noise process. This scheme is compared with the MEWMA control chart of Lowry et al. (1992) applied to the residuals. By an extensive Monte carlo study the ARL of both charts are determined for several multivariate autoregressive processses.