This research studies regression methods in time series settings with periodic properties. The general goal of this work is to put statistical inference for regression models with periodic error disturbances on the same footing as that for its stationary brethren. The particular issues examined include (1) simple linear regression for periodic series, (2) analysis of variance methods for periodic series, (3) undocumented changepoint detection in periodic series, (4) the adjustment of periodic series for documented and undocumented changepoint times, and (5) trends in monthly extreme temperatures, and winter snow depths. The work will advance and further connect the statistical areas of time series, forecasting, extreme value analysis, and regression modeling.
On a practical level, the research will help resolve climate change issues within the United States and, more generally, help quantify global warming. The statistical methods developed will be used to study trends in United States monthly extreme (maximum and minimum) and average temperatures. Trends in United States snow cover (over seasonal maximums and snow water equivalent) will also be examined