Mathematics Colloquium: Some Changepoint Problems and their Uses in Climatology

2012-03-20

4:10 pm Neill Hall 5W

Robert Lund, Clemson University

This talk overviews changepoint issues in climate studies. Changepoints are ubiquitous features in climatic time series, occurring whenever stations relocate or gauges are changed. Ignoring changepoints can produce spurious conclusions. Changepoint tests involving cumulative sums, likelihood ratio, and maximums of F statistics are introduced; the asymptotic distributions of these statistics are quantified under the changepoint-free null hypothesis. We find that cumulative sum procedures work best when the changepoint is near the center of the data record; otherwise, maximums of F statistics perform better. Next, time series aspects of the problem are addressed. Series with positive autocorrelation can have long sojourns above and below mean levels, hence mimicing a mean shift. We show how to modify the above methods to account for autocorrelation. Finally, multiple changepoint problems in autocorrelated settings are studied. Here, a minimum description length criterion is devised to estimate the location and times of the changepoints.