Periodic ARMA Modeling

周期性在涉及潮汐、气候学、生态学、社会学、天文学、经济学、水文学等的数据中自然产生。本文研究了一般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，简约周期时间序列模型的发展，变点和齐次方法，以及月平均和极端温度下的趋势特性。数学和统计方法以周期自回归滑动平均模型(PARMA)时间序列模型为中心--周期序列的基本建模工具。将探索一种计算Parma模型自协方差结构的有效算法。还将研究周期序列的变点和均匀方法，这是天气记录站移动时出现的一个问题。发展的数学和统计结果被用于解决气候问题。将对美国气象站的月平均气温和极端气温的趋势进行研究。这项详细的研究将加深我们对气候变化和全球变暖的理解。变点方面可能是数据最重要的特征。需要对数据中自协方差的周期性进行简约建模，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，这些方法还改进了对周期序列的预测。

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.