Description
TitleNew models and methods for time series analysis in big data era
Date Created2015
Other Date2015-05 (degree)
Extent1 online resource (xiii, 124 p. : ill.)
DescriptionIn big data era, available information becomes massive and complex and is often observed over time. Conventional time series models are limited in capability of dealing with these type of data. This dissertation focuses on developing new statistical models, along with their associated estimation procedures, to analyze time series data in functional form, and in high dimension, with linear or nonlinear dynamics, which can be broadly applicable to finance, environment, engineering, biological and medical sciences. Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who worst introduced the functional autoregressive (FAR) models, we propose a convolutional functional autoregressive (CFAR) model, where the function at time t is a result of the sum of convolutions of the past functions with a set of convolution functions, plus a noise process, mimicking the autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. We adopt a sieve estimation procedure based on the B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. As for high-dimensional time series data, dimension reduction is an important issue and can be effectively performed by factor analysis. Considering the factor impacts may vary under different conditions, we propose a factor model with regime-switching mechanism, allowing loadings to change across regimes, and combined eigendecomposition and Viterbi algorithm for estimation. We discover that, with multiple states of different 'strength', the convergence rate of loading matrix estimator for strong states is the same as the one-regime case, while the rate improves for weak states, gaining extra information from strong states. The theoretical properties of the procedure are investigated as well. In addition, we propose a new class of nonparametric seasonal time series models under the framework of the functional coefficient model. The coefficients in the proposed model change over time and consist of the trend and seasonal components to characterize seasonality. A local linear approach is developed to estimate the nonparametric trend and seasonal effect functions. The proposed methodologies are illustrated by two simulated examples and the model is applied to characterizing the seasonality of the monthly number of tourists visiting Hawaii.
NotePh.D.
NoteIncludes bibliographical references
Noteby Xialu Liu
Genretheses, ETD doctoral
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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