Analysis of Periodic Time Series

本研究考虑周期时间序列及其在气候学问题上的应用。由于天气、潮汐、太阳辐射和其他自然循环过程的周期性，许多相关的时间序列在其统计结构中继承了周期性。本文探讨了周期序列分析中的一些常见问题。具体研究的是何时将时间序列视为周期序列，如何对周期序列进行建模，如何估计周期序列的趋势，以及如何准确预测周期序列的未来值。为了解决这些问题，研究了周期自回归移动平均时间序列模型的数学性质。分析的主要工具是时间序列创新算法，该算法利用所考虑的周期模型的导出协方差结构来计算模型的似然和最佳线性预测。所开发的数学和统计结果用于研究当前的一些气候问题。特别是，已发展的趋势估计技术应用于北美温度趋势的研究。将周期性月度序列的趋势估计值与平稳年度序列的趋势估计值进行比较。由于年序列是通过对月序列取平均值得到的——序列长度减少了12倍——因此从月序列得出的趋势估计更为准确。这有助于更好地理解气候变化和全球变暖。同样，发展起来的预报方法对气候过程的预报也有所改进。

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.