Estimation of structural breaks in nonstationary time series
Date
2008
Journal Title
Journal ISSN
Volume Title
Abstract
Many time series exhibit structural breaks in a variety of ways, the most obvious being a mean level shift. In this case, the mean level of the process is constant over periods of time, jumping to different levels at times called change-points. These jumps may be due to outside influences such as changes in government policy or manufacturing regulations. Structural breaks may also be a result of changes in variability or changes in the spectrum of the process. The goal of this research is to estimate where these structural breaks occur and to provide a model for the data within each stationary segment. The program Auto-PARM (Automatic Piecewise AutoRegressive Modeling procedure), developed by Davis, Lee, and Rodriguez-Yam (2006), uses the minimum description length principle to estimate the number and locations of change-points in a time series by fitting autoregressive models to each segment. The research in this dissertation shows that when the true underlying model is segmented autoregressive, the estimates obtained by Auto-PARM are consistent. Under a more general time series model exhibiting structural breaks, Auto-PARM's estimates of the number and locations of change-points are again consistent, and the segmented autoregressive model provides a useful approximation to the true process. Weak consistency proofs are given, as well as simulation results when the true process is not autoregressive. An example of the application of Auto-PARM as well as a source of inspiration for this research is the analysis of National Park Service sound data. This data was collected by the National Park Service over four years in around twenty of the National Parks by setting recording devices in several sites throughout the parks. The goal of the project is to estimate the amount of manmade sound in the National Parks. Though the project is in its initial stages, Auto-PARM provides a promising method for analyzing sound data by breaking the sound waves into pseudo-stationary pieces. Once the sound data have been broken into pieces, a classification technique can be applied to determine the type of sound in each segment.
Description
Rights Access
Subject
autoregression
minimum description length
structural breaks
statistics