Regression with Periodic Series

摘要DMS-0304407 PI：Robert B。LundThis research studies regression methods in time series settings with periodic properties.这项工作的总体目标是把统计推断的回归模型与定期误差干扰的同一基础上，其固定的兄弟。研究的具体问题包括（1）周期序列的简单线性回归，（2）周期序列的方差分析方法，（3）周期序列中未记录的变点检测，（4）记录和未记录的变点时间的周期序列调整，以及（5）每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连接时间序列、预测、极值分析和回归建模等统计领域。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。所开发的统计方法将用于研究美国每月极端（最高和最低）和平均温度的趋势。还将审查美国积雪趋势（超过季节性最大值和雪水当量）

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