Periodic ARMA Modeling

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

Robert B. Lund Periodic ARMA Modeling, DMS 0071383 Abstract Periodicities naturally arise in data involving tides, climatology, ecology, sociology, astronomy, economics, hydrology, etc.. This research studies general periodic time series modeling methods along with some applications to climatological problems. The specific questions examined here include efficient computation of the autocovariance structure of periodic time series models, parsimonious periodic time series model development, changepoint and homogeneity methods, and trend properties in monthly average and extreme temperatures. The mathematical and statistical methods center on periodic autoregressive moving average models (PARMA) time series models - the fundamental modeling vehicle for periodic series. An efficient algorithm to compute the autocovariance structure of a PARMA model will be explored. Changepoint and homogeneity methods for periodic series, an issue that arises when weather recording stations move, will also be investigated. The developed mathematical and statistical results are used to settle some climatological problems. A study of the trends in monthly temperature means and extremes from United States stations will be conducted. This detailed study will enhance our understanding of climate change and global warming. The changepoint aspect is perhaps the data's most important feature. Periodicities in the autocovariances in the data need to be parsimoniously modeled to compute accurate standard errors. Standard errors are needed to gauge the reliability of the computed trends. The methods also yield improved forecasts of periodic series as a byproduct.