Parameter estimation of smooth threshold autoregressive models.
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This thesis is mainly concerned with the estimation of parameters of a first-order Smooth Threshold Autoregressive (STAR) model with delay parameter one. The estimation procedures include classical and Bayesian methods from a parametric and a semiparametric point of view.As the theoretical importance of stationarity is a primary concern in estimation of time series models, we begin the thesis with a thorough investigation of necessary or sufficient conditions for ergodicity of a first-order STAR process followed by the necessary and sufficient conditions for recurrence and classification for null-recurrence and transience.The estimation procedure is started by using Bayesian analysis which derives posterior distributions of parameters with a noninformative prior for the STAR models of order p. The predictive performance of the STAR models using the exact one-step-ahead predictions along with an approximation to multi-step-ahead predictive density are considered. The theoretical results are then illustrated by simulated data sets and the well- known Canadian lynx data set.The parameter estimation obtained by conditional least squares, maximum likelihood, M-estimator and estimating functions are reviewed together with their asymptotic properties and presented under the classical and parametric approaches. These estimators are then used as preliminary estimators for obtaining adaptive estimates in a semiparametric setting. The adaptive estimates for a first-order STAR model with delay parameter one exist only for the class of symmetric error densities. At the end, the numerical results are presented to compare the parametric and semiparametric estimates of this model.
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Livingston, G.; Nur, Darfiana (2019)The multivariate smooth transition autoregressive model with order k (M-STAR)(k) is a nonlinear multivariate time series model able to capture regime changes in the conditional mean. The main aim of this paper is to develop ...
Chan, Felix ; Theoharakis, B. (2009)© MODSIM 2009.All rights reserved. It is well known in the literature that the joint parameter estimation of the Smooth Autoregressive - Generalized Autoregressive Conditional Heteroskedasticity (STAR-GARCH) models poses ...
Livingston, G.; Nur, Darfiana (2018)© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. The smooth transition autoregressive (STAR)(k)–GARCH(l, m) model is a non-linear time series model that is able to account for changes in both regime and ...