Time Series Models: Sparsity, Mis-specification and Forecasting

以固定的时间间隔收集大量数据，如股票价格或各种类型的天气测量。通常可以对同一时间单位进行相互关联的测量，例如每日股票开盘、收盘、高价和低价，这些数据是多时间序列的例子。有时空间维度也提供重要的信息，需要时空统计模型。******每日天气数据，包括最高和最低温度、总降水量、平均湿度和其他变量，是一个多时间序列的例子，可在一个地区的各个站点获得。在大气-海洋耦合全球环流模式（AOGCM）生成的各种可能的气候变化情景下的未来天气情景，对土木工程师和其他人员在制定应对气候变化对现有水库系统和重要基础设施影响的计划时很有意义。我的研究将集中于发展区域气象站时间序列的时空统计模型，并将这些模型与AOGCM的输出联系起来，以便模拟未来可能的天气情景，以供规划之用。目前广泛使用的PC技术和免费的编程环境R已经证明了我对这些时空数据的初步工作是成功的。******除了这些具体的时间序列模型构建应用，我的研究将进一步发展时间序列分析领域。时间序列的诊断检查对于理解模型可能的局限性以及模型制定中可能的错误对预测和其他推论的影响非常重要。改进的诊断检查和见解正在开发中。******在许多数量级上变化的数据，如地震，通常以转换后的尺度（如对数）报告。在时间序列的统计模型中，还有许多其他有用的简化转换。但是对于许多操作目的，我们需要未转换域中的数据。我的研究将开发在未转换数据域中使用一般损失函数进行精确预测的方法。******环境时间序列，如水或空气质量，由于技术限制经常被审查。考虑到这一点并获得最佳预测的精确建模方法对监测环境的机构很重要。我们的方法，示例和免费提供的软件将在适当的统计期刊上发表。******高维时间序列出现在视频医学成像。在许多其他的例子中，训练一个分类器来预测时间序列属于K个可能的组中的哪一个是很有趣的。这是时间序列聚类问题。我将开发一些时间序列分类的新工具。

A large quantity of data is collected at regular time intervals such as stock prices or weather measurements of various types. Often inter-related measurements at for the same time unit are available such as with daily stock open, close, high and low prices and such data are examples of multiple time series. Sometimes the spatial dimension also provides important information and space-time statistical models are required.******Daily weather data, which may include maximum and minimum temperature, total precipitation, average humidity and other variables, is an example of a multiple time series which is available at various stations in a region. Future weather scenarios under various possible climate change scenarios generated by the Atmosphere-Ocean coupled Global Circulation Model (AOGCM) are of interest to civil engineers and others in making plans to deal with impact of climate change on existing reservoir systems and important infrastructure. My research will focus on developing space-time statistical models for regional weather station time series and linking these models with the outputs from the AOGCM so that possible future weather scenarios may be simulated for planning purposes. Current widely available PC technology with the freely available programming environment R has already proved successful in my preliminary work with such space-time data.******In addition to these specific time series model building applications, my research will further develop the field of time series analysis. Diagnostic checks for time series are important for understanding possible limitations of the models and also what the effect of possible errors in the model formulation have on predictions and other inferences. Improved diagnostic checks and insights are in development.******Data which vary through many orders of magnitude, such as earthquakes, are often reported on a transformed scale, such as logarithms. There are many other such useful and simplifying transformations that are commonly used in statistical models for time series. For many operational purposes though we need the data in the untransformed domain. My research will develop methods for exact prediction with general loss functions in the untransformed data domain.******Environmental time series, such as water or air quality, are frequently censored due to technological limitations. Exact modelling methods for taking this into account and obtaining optimal predictions are important for agencies that monitor the environment. Our methodology, with examples and freely available software will be published in suitable statistical journals.******High dimensional time series arise in video medical imaging. There are many other examples where it is of interest to train a classifier to predict which of say K possible groups a time series belongs to. This is the time series clustering problem. I will be developing some new tools for time series classification.