THESIS
2020
xii, 135 pages : illustrations ; 30 cm
Abstract
This thesis considers multivariate heavy-tailed nonstationary time series models
and the structure-changed threshold double autoregressive (TDAR) models. The
first part develops an automated approach to determine the cointegrating rank,
lag order and estimate parameters simultaneously in the vector error correction
(VEC) model with heavy-tailed innovations. In the second part, the asymptotic
theories of the full rank least squares estimator (FLES) and reduced rank least
squares estimator (RLSE) of heavy-tailed and nonstationary autoregressive and
moving average (ARMA) models are given. This thesis also investigates the
asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of
structure changed and two-regime TDAR models. It is shown that both the
estimated thre...[
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This thesis considers multivariate heavy-tailed nonstationary time series models
and the structure-changed threshold double autoregressive (TDAR) models. The
first part develops an automated approach to determine the cointegrating rank,
lag order and estimate parameters simultaneously in the vector error correction
(VEC) model with heavy-tailed innovations. In the second part, the asymptotic
theories of the full rank least squares estimator (FLES) and reduced rank least
squares estimator (RLSE) of heavy-tailed and nonstationary autoregressive and
moving average (ARMA) models are given. This thesis also investigates the
asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of
structure changed and two-regime TDAR models. It is shown that both the
estimated threshold and change-point are n-consistent, and they converge weakly
to the smallest minimizer of a compound Poisson process and the location of
minima of a two-sided random walk, respectively. Simulation studies and real
examples are given to evaluate the performance of our methods.
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