Time Series Models: Sparsity, Mis-specification and Forecasting

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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.