Themes in Time Series Analysis

时间序列是连续数据值的序列。我使用过的例子包括股票的收盘价、气象站的平均日温度、指定位置的月平均平流层臭氧、每月因特定情况向肾病医生就诊的次数、每天深夜车祸、连续的心跳间歇以及许多其他情况。我开发的时间序列方法被用来预测平流层臭氧恢复到以前水平的年数(技术计量学，DOI=10.1.1.144.6621)。我目前的研究涉及检测周期性的基因表达时间序列的模型和被审查的水质时间序列的模型。某些时间序列可能表现出很强的持续自相关性，例如特定位置的每小时风速。对这种强持续序列，特别是短时间序列的检测和建模是当前的另一个研究领域。许多地区气象站的日平均降水量和气温连续多年可用。考虑到区域、季节和长期趋势的这种多时间序列的建模是我参与的一项活跃的研究，它应用于水资源和水库系统的管理、森林火灾研究，并用于全球气候变化模型的缩小尺度。提出了一种新的自动多元谱分析方法。还发现了一种有趣的新类型的无意义关联，它可能会使许多类型的统计模型中的推论无效。提出了一种检测并修复此问题的方法。

Time series are sequences of consecutive data values. Example that I have worked with include the close price for a stock, mean daily temperature at a weather station, monthly average stratospheric ozone at a specified location, monthly number of consultations to a nephrologist for a specific condition, daily late-night automobile fatalities, successive heart interbeat intervals and many others. A time series method I developed was used to predict the number of years for stratospheric ozone to return to its previous levels (Technometrics, doi = 10.1.1.144.6621). My current research involves models for time series of gene expressions to detect periodicity and models for censored water quality time series. Some time series may exhibit strongly persistent autocorrelation as with hourly wind speed at a specific location. The detection and modeling of such strongly persistent series particularly with short time series is another current research area. Daily mean precipitation and temperature are available for many years at many regional weather stations. The modeling of such multiple time series taking into account the regional, seasonal and long term trend is an active research that I am involved in and it has applications for the management of water resources and reservoir systems, forest fire research and for use in downscaling with global climate change models. A new method for automatic multivariate spectral analysis is suggested. An interesting new type of nonsense correlation has also been discovered that can potentially invalidate the inferences in many types of statistical models. A method for detecting this problem and fixing it is being proposed.