Periodic ARMA Modeling

周期ARMA模型，DMS 0071383abstract涉及潮汐、气候学、生态学、社会学、天文学、经济学、水文学等领域的数据自然存在周期性。本文研究了一般的周期时间序列建模方法及其在气候学问题中的应用。本文研究的具体问题包括周期时间序列模型自协方差结构的有效计算、周期时间序列模型的简化、变点和同质性方法以及月平均和极端温度的趋势特性。数学和统计方法以周期自回归移动平均模型（PARMA）时间序列模型为中心，该模型是周期序列的基本建模工具。本文将探讨一种计算PARMA模型自协方差结构的有效算法。变化点和均匀方法的周期性序列，一个问题出现时，天气记录站的移动，也将进行调查。发展的数学和统计结果被用来解决一些气候学问题。美国气象站将对每月平均温度和极端温度的趋势进行研究。这项详细的研究将增强我们对气候变化和全球变暖的认识。变更点方面可能是数据最重要的特性。数据中自协方差的周期性需要简化建模以计算准确的标准误差。需要标准误差来衡量计算趋势的可靠性。作为副产品，这些方法还能改进周期序列的预测。

Robert B. LundPeriodic ARMA Modeling, DMS 0071383AbstractPeriodicities naturally arise in data involving tides, climatology,ecology, sociology, astronomy, economics, hydrology, etc.. This researchstudies general periodic time series modeling methods along with someapplications to climatological problems. The specific questions examinedhere include efficient computation of the autocovariance structure ofperiodic time series models, parsimonious periodic time series modeldevelopment, changepoint and homogeneity methods, and trend properties inmonthly average and extreme temperatures. The mathematical andstatistical methods center on periodic autoregressive moving averagemodels (PARMA) time series models - the fundamental modeling vehicle forperiodic series. An efficient algorithm to compute the autocovariancestructure of a PARMA model will be explored. Changepoint and homogeneitymethods for periodic series, an issue that arises when weather recordingstations move, will also be investigated. The developed mathematical and statistical results are used to settlesome climatological problems. A study of the trends in monthlytemperature means and extremes from United States stations will beconducted. This detailed study will enhance our understanding ofclimate change and global warming. The changepoint aspect is perhapsthe data's most important feature. Periodicities in the autocovariancesin the data need to be parsimoniously modeled to compute accuratestandard errors. Standard errors are needed to gauge the reliability ofthe computed trends. The methods also yield improved forecasts ofperiodic series as a byproduct.