Trend and Variable-Phase Seasonality Estimation from Functional Data
The problem of estimating trend and seasonality has been studied over several decades, although mostly using single time series setup. This dissertation studies the problem of estimating these components from a functional data point of view, i.e. multiple curves, in situations where seasonal effects...
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| Format: | Others |
| Language: | English English |
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Florida State University
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| Online Access: | http://purl.flvc.org/fsu/fd/FSU_2017SP_Tai_fsu_0071E_13816 |
| Summary: | The problem of estimating trend and seasonality has been studied over several decades, although mostly using single time series setup. This dissertation studies the problem of estimating these components from a functional data point of view, i.e. multiple curves, in situations where seasonal effects exhibit arbitrary time warpings or phase variability across different observations. Rather than ignoring the phase variability, or using an off-the-shelf alignment method to remove phase, we take a model-based approach and seek Maximum Likelihood Estimators (MLEs) of the trend and the seasonal effects, while performing alignments over the seasonal effects at the same time. The MLEs of trend, seasonality, and phase are computed using a coordinate descent based optimization method. We use bootstrap replication for computing confidence bands and for testing hypothesis about the estimated components. We also utilize log-likelihood for selecting the trend subspace, and for comparisons with other candidate models. This framework is demonstrated using experiments involving synthetic data and three real data (Berkeley growth velocity, U.S. electricity price, and USD exchange fluctuation). Our framework is further applied to another biological problem, significance analysis of gene sets of time-course gene expression data and outperform the state-of-the-art method. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Spring Semester 2017. === April 11, 2017. === curves registration, functional data analysis, time warpings, Trend and seasonality estimation === Includes bibliographical references. === Kyle A. Gallivan, Professor Co-Directing Dissertation; Anuj Srivastava, Professor Co-Directing Dissertation; Wei Wu, University Representative; Eric P. Klassen, Committee Member; Giray Okten, Committee Member. |
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