Analysis of Periodic Time Series

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Lund 9703838 This research considers periodic time series and their applications to problems in climatology. Because of the periodic nature of weather, tides, solar radiation, and other naturally cyclic processes, many related time series inherit periodicities in their statistical structure. This research investigates some common questions of analysis involving periodic series. Specifically examined are when a time series should be regarded as periodic, how a periodic series should be modeled, how to estimate trends in periodic series, and how to accurately forecast future values of periodic series. To settle these questions, mathematical properties of periodic autoregressive moving-average time series models are explored. The main tool of analysis is the time series Innovations Algorithm, which uses the derived covariance structure of the periodic models being considered to compute model likelihoods and best linear predictors. The mathematical and statistical results developed are used to investigate some current climatological issues. In particular, the developed trend estimation techniques are applied in a study of North American temperature trends. Trend estimates of periodic monthly series are compared to trend estimates of stationary yearly series. Since the yearly series are obtained by averaging the monthly series - a twelvefold series length reduction - the trend estimates from the monthly series are more accurate. This results in a better understanding of climatic change and global warming. Likewise, the developed prediction methods yield improved forecasts of climatological processes.