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Stationary time series resulting from certain positive definite kernels and simulation via high-order vector autoregressive models
Ma, Nicholas
Ma, Nicholas
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t13028_Ma.pdf
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2013-05
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Thesis
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Electronic dissertations
Electronic dissertations
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Abstract
Vector auto-regressive models have traditionally been used to model and forecast
multivariate time series data, predicting future values based on previous observations. In this
thesis, we introduce some multivariate time series with power-law decaying covariance matrix
functions, and then construct a VAR model in order to generate approximate data from that
time series. A fast model is developed to solve for the VAR(p) coefficients, implementing
a block-Toeplitz equation solver to enable the choice of large p, avoiding the memory and
speed issues with solving large systems via Gaussian elimination. An approximate error
bound is established, demonstrating the quality of the simulation for large p. Finally, we
explore inverting the VAR model to obtain a VMA (vector moving average) model.
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Thesis (M.S.)--Wichita State University, Fairmount College of Liberal Arts and Sciences, Dept. of Mathematics, Statistics and Physics
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Wichita State University
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Copyright Nicholas Ma, 2013.