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Modeling Nonstationarity Using Locally Stationary Basis Processes

Ganguly, Shreyan
http://rave.ohiolink.edu/etdc/view?acc_num=osu1563408374215259

Abstract Details

2019, Doctor of Philosophy, Ohio State University, Statistics.
Methods of estimation and forecasting for stationary models are well known and straightforward in classical time series analysis. For this reason, time series analysis involves using mathematical transformations to render the stochastic process approximately stationary and conduct inference on the transformed series. However, assuming stationarity, even for the transformed series, is at best an idealization. In practice, this assumption may be unrealistic, especially for processes with time varying statistical properties. We define a class of locally stationary processes called locally stationary basis (LSB) processes which can lead to more accurate uncertainty quantification over making an invalid assumption of stationarity. LSB processes assumes the model parameters to be time-varying and parameterizes them in terms of a transformation of basis functions. The transformation is required as it ensures that the processes are locally stationary, and as required, causal, invertible or identifiable, something that is generally ignored while defining locally stationary models. We develop methods and theory for parameter estimation in this class of models, and propose a test that allow us to examine certain departures from stationarity. We assess our methods using simulation studies and apply these techniques to the analysis of an electroencephalogram time series. We also extend our theory for LSB processes to the spatio-temporal case, in particular, LSB spatio-temporal processes. While there are several models in literature which explore the non-stationarities in the spatial domain, few have been developed for non-stationarities in time, while still maintaining space-time interactions. We give an overview of the theory for LSB processes and provide a Bayesian framework for carrying out inference with such models along with spatial predictions. A suitable algorithm is proposed for efficient posterior simulation for this class of models. We use this model to for an analysis of the monthly mean temperatures from the Global Historical Climatology Network data in and around the state of Ohio, USA from 1905-2004.
Peter Craigmile (Advisor)
Christopher Hans (Committee Member)
Lo-Bin Chang (Committee Member)
148 p.
Statistics
Time varying processes; Basis functions; Tests of stationarity; Causality; Parameter estimation; Uncertainty quantification; EEG; Mean temperatures; Climate data; Bayesian; MCMC

Recommended Citations

Citations

  • Ganguly, S. (2019). Modeling Nonstationarity Using Locally Stationary Basis Processes [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1563408374215259

    APA Style (7th edition)

  • Ganguly, Shreyan. Modeling Nonstationarity Using Locally Stationary Basis Processes. 2019. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1563408374215259.

    MLA Style (8th edition)

  • Ganguly, Shreyan. "Modeling Nonstationarity Using Locally Stationary Basis Processes." Doctoral dissertation, Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1563408374215259

    Chicago Manual of Style (17th edition)

osu1563408374215259
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This open access ETD is published by The Ohio State University and OhioLINK.