Bayesian estimation for threshold autoregressive model with multiple structural breaks
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Bayesian estimation for threshold autoregressive model with multiple structural breaks Varun Agiwal1
· Jitendra Kumar1
Received: 23 July 2019 / Accepted: 25 September 2020 © Sapienza Università di Roma 2020
Abstract This paper provides a Bayesian setup for multiple regimes threshold autoregressive model with possible break points. A full conditional posterior distribution is obtained for all model parameters with considering suitable prior information. Threshold and break point variables do not attain standard form distributions. To compute posterior distributions, we apply the Gibbs sampler with the Metropolis-Hastings algorithm. A variety of loss functions are considered for optimizing the risk associated with each parameter. For empirical evidence, simulation study and real data illustration are carried out. Keywords Threshold autoregressive model · Bayesian Inference · MCMC method · Structural Break Mathematics Subject Classification 62F15 · 37M10
1 Introduction Linear time series models are very popular to investigate the dynamic structure of a series over time. These models are well established in literature to adequately recognize the process efficiency and explore the characteristics such as stationarity, unit root, de-trending, cointegration, etc. and then provide improved prediction (see [13,14,22,28]). However, in many situations, it becomes difficult to identify by visual inspection whether apparent non-linear behavior of the series is due to stochastic trend or due to non-linearity in parameters. Such a non-linearity in parameters often arises during the permanent change (structural break), temporary effect (outlier) or varying structure relationship. For these reasons, a range of non-linear time series models are introduced for a better inference. The issue of structural break in various univariate and multivariate time series models was addressed by [1–3,21,27] for detection, estimation and testing purposes.
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Jitendra Kumar [email protected] Varun Agiwal [email protected]
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Department of Statistics, Central University of Rajasthan, Ajmer, Rajasthan, India
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V. Agiwal, J. Kumar
Most of the available literature on structural break considers parameter changes on the time horizon. However, in time series modelling, series concerns change on both time and parameters due to its own past realizations that categorize into linear and non-linear models. Tong [25,26] introduced a standard non-linear time series model, known as threshold autoregressive (TAR) model, and Chan [5] derived the limiting distribution of least squares estimators of TAR parameters. Gonzalo and Wolf [17] proposed a sub-sampling methodology to obtain the consistent confidence interval for the threshold and regression parameters when the model is discontinuous. Liu et al. [20] considered the least squares estimation to estimate the parameter of non-stationary first order TAR model and obtained its limiting distribution. Li et al. [19] extended Liu et al. [20] work for the threshold autoregressive moving average
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