Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process
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Bayesian Estimation and Unit Root Test for Logistic Smooth Transition Autoregressive Process Anoop Chaturvedi1 · Shivam Jaiswal1
© The Indian Econometric Society 2019
Abstract The paper considers nonlinear logistic smooth transition autoregressive (LSTAR) process and aims to detect the unit root under the null hypothesis of a random walk process against the alternative of a stationary LSTAR process and to estimate the parameters of the process in Bayesian framework using MCMC. The simulation study is carried out for investigating the performance of the Bayes estimators for parameters and Bayesian unit root test and it has been observed that the estimates of parameters of the LSTAR process are close to the true parameter values. It has been observed that the Bayesian unit root test performs well and the power of the test is high even for the boundary cases having root close to unity, at least when the sample size is large. Since the LSTAR models are widely applied for real exchange rate modeling, the theoretical results are illustrated empirically for the real exchange rates of ten OCED countries. Keywords LSTAR process · Unit root · Model comparison · Parameter estimation · Bayes factor · MCMC JEL Classification C220
Introduction The nonlinear dynamics exhibited by several time series is often characterized by switches from one regime to another regime. Such behavior of regime switching can be elucidated using different regime switching time series models such as threshold autoregressive (TAR) model (Tong 1978), smooth transition autoregressive (STAR) model (Chan and Tong 1986), Markov switching autoregressive (MSAR) model * Anoop Chaturvedi [email protected] Shivam Jaiswal [email protected] 1
Department of Statistics, University of Allahabad, Allahabad, UP, India
13
Vol.:(0123456789)
Journal of Quantitative Economics
(Hamilton 1989). Teräsvirta (1994) considered two different types of STAR models; viz., the logistic STAR (LSTAR) model and exponential STAR (ESTAR) model. van Dijk et al. (2002) surveyed the developments in STAR models and its different variants. They pointed out that in LSTAR models, the two regimes are associated with small and large values of the transition variable, and this type of regime-switching is convenient for modelling, for instance, the business cycle asymmetry to distinguish expansions and recessions. Teräsvirta and Anderson (1992) applied LSTAR models for characterizing different dynamics of industrial production indices in a number of OECD countries during expansions and recessions. Hall et al. (2001) applied LSTAR model to explain the most turbulent period in El Niño events. Deschamps (2008) explored LSTAR and MSAR models to explain the US unemployment rate. Arango and Gonzalez (2001) modeled different measures of annual inflation in Colombia using LSTAR and ESTAR models. Buncic (2017) recently observed that the exponential function is ill-suited as a regime weighting function as (1) it has identification problem with respect to the transition func
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