Structural Break Estimation in Time Series: Theory and Practice

Abstract

The program Auto-PARM (Automatic Piecewise AutoRegresive Modeling), developed by Davis, Lee, and Rodriguez-Yam (2006), uses the minimum description length (MDL) principle to estimate the number and locations of change-points in a time series by fitting autoregressive models to each segment. When the number of change-points is known, Davis et al. (2006) show that the (relative) change-point location estimates are consistent when the true underlying model is segmented autoregressive. In this paper, we show that the estimates of the number of change-points and the autoregressive orders obtained by minimizing the MDL are consistent for the true values when using conditional maximum (Gaussian) likelihood variance estimates. However, if Yule-Walker variance estimates are used, the estimate of the number of change-points is not necessarily consistent. This surprising result is due to an exact cancellation of first-order terms in a Taylor series expansion in the conditional maximum likelihood case, which does not occur in the Yule-Walker case. We will illustrate the use of Auto-PARM in a variety of examples and then describe some of theoretical issues associated with AutoPARM. (The theory part is joing with Stacey Hancock and Yi-Ching Yao.)