Regression with Periodic Series

摘要DMS-0304407PI：Robert B.Lund本研究在具有周期性的时间序列背景下的回归方法。这项工作的总体目标是使具有周期误差扰动的回归模型的统计推断与其平稳同胞模型的统计推断处于相同的地位。审查的具体问题包括：(1)周期序列的简单线性回归，(2)周期序列的方差分析，(3)周期序列中未记录的变点检测，(4)对有记录和无记录的变点时间的周期序列的调整，以及(5)月极端温度和冬季积雪深度的趋势。这项工作将推进并进一步将时间序列、预测、极值分析和回归建模等统计领域联系起来。在实践层面上，这项研究将有助于解决美国国内的气候变化问题，更广泛地说，有助于量化全球变暖。开发的统计方法将用于研究美国每月极端(最高和最低)和平均气温的趋势。还将研究美国积雪的趋势(超过季节最大值和雪水当量)。

AbstractDMS-0304407PI: Robert B. LundThis research studies regression methods in time series settings with periodic properties. The general goal of this work is to put statistical inference for regression models with periodic error disturbances on the same footing as that for its stationary brethren. The particular issues examined include (1) simple linear regression for periodic series, (2) analysis of variance methods for periodic series, (3) undocumented changepoint detection in periodic series, (4) the adjustment of periodic series for documented and undocumented changepoint times, and (5) trends in monthly extreme temperatures, and winter snow depths. The work will advance and further connect the statistical areas of time series, forecasting, extreme value analysis, and regression modeling.On a practical level, the research will help resolve climate change issues within the United States and, more generally, help quantify global warming. The statistical methods developed will be used to study trends in United States monthly extreme (maximum and minimum) and average temperatures. Trends in United States snow cover (over seasonal maximums and snow water equivalent) will also be examined