Time Series Models: Sparsity, Mis-specification and Forecasting

有规律的时间间隔收集了大量数据，例如股票价格或各种天气测量。通常，同一时间单位的相互关联的测量是可用的，例如每日股票开盘、收盘、高和低价格，这样的数据是多个时间序列的例子。有时空间维度也提供了重要的信息，需要时空统计模型。*每日天气数据可能包括最高和最低温度、总降雨量、平均湿度和其他变量，是一个地区不同站点提供的多时间序列的一个例子。由大气-海洋耦合全球环流模式(AOGCM)产生的各种可能的气候变化情景下的未来天气情景是土木工程师和其他人在制定计划以应对气候变化对现有水库系统和重要基础设施的影响时感兴趣的。我的研究将集中于开发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，以便为规划目的模拟未来可能出现的天气情景。目前广泛使用的PC技术和免费可用的编程环境R已经在我对这样的时空数据的初步工作中被证明是成功的。*除了这些具体的时间序列建模应用之外，我的研究将进一步发展时间序列分析领域。对时间序列的诊断检查对于了解模型的可能局限性以及模型公式中可能的错误对预测和其他推断的影响是重要的。改进的诊断检查和洞察正在开发中。*不同量级的数据，如地震，经常以转换后的标度报告，如对数。在时间序列的统计模型中通常使用许多其他这样的有用和简化的变换。但是，出于许多操作目的，我们需要未转换域中的数据。我的研究将开发在未变换的数据域中使用一般损失函数进行准确预测的方法。*环境时间序列，如水或空气质量，由于技术限制而经常被审查。考虑到这一点并获得最佳预测的准确建模方法对于监测环境的机构来说很重要。我们的方法、实例和免费软件将发表在合适的统计期刊上。*高维时间序列出现在视频医学成像中。还有许多其他的例子，其中训练分类器以预测时间序列属于例如K个可能的组中的哪一个是感兴趣的。这就是时间序列的聚类问题。我将开发一些用于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.