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.
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References
Albert, J.H., Chib, S.: Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. J. Bus. Econ. Stat. 11(1), 1–15 (1993)
Bai, J., Perron, P.: Estimating and testing linear models with multiple structural changes. Econometrica 66(1), 47–78 (1998)
Barnett, G., Kohn, R., Sheather, S.: Bayesian estimation of an autoregressive model using Markov chain Monte Carlo. J. Econ. 74(2), 237–254 (1996)
Casella, G., George, E.I.: Explaining the Gibbs sampler. Am. Stat. 46, 167–174 (1992)
Chan, K.S.: Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Ann. Stat. 21(1), 520–533 (1993)
Charif, M.A.I.H.A.: Bayesian inference for threshold moving average models. Metron 61(1), 119–132 (2003)
Chen, C.W.S.: A Bayesian analysis of generalized threshold autoregressive models. Stat. Prob. Lett. 40(1), 15–22 (1998)
Chen, C.W.S., Gerlach, R., Liu, F.C.: Detection of structural breaks in a time varying heteroskedastic regression model. J. Stat. Plann. Inference 141, 3367–3381 (2011)
Chen, C.W.S., Lee, J.C.: Bayesian inference of threshold autoregressive models. J. Time Ser. Anal. 16(5), 483–492 (1995)
Chen, C.W.S., Liu, F.C., Gerlach, R.: Bayesian subset selection for threshold autoregressive moving-average models. Comput. Stat. 26(1), 1–30 (2011)
Chib, S., Greenberg, E.: Understanding the Metropolis-hastings algorithm. Am. Stat. 49, 327–335 (1995)
De Wachter, S., Tzavalis, E.: Detection of structural breaks in linear dynamic panel data models. Comput. Stat. Data Anal. 56(11), 3020–3034 (2012)
Dickey, D.A., Fuller, W.A.: Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 74(366a), 427–431 (1979)
Engle, R.F., Granger, C.W.J.: Co-integration and error-correction: representation, estimation, and testing. Econometrica 55, 251–276 (1987)
Gao, Z., Ling, S.: Statistical inference for structurally changed threshold autoregressive models. Stat. Sin. 29, 1803–1829 (2018)
Geweke, J., Terui, N.: Bayesian threshold autoregressive models for nonlinear time series. J. Time Ser. Anal. 14(5), 441–454 (1993)
Gonzalo, J., Wolf, M.: Subsampling inference in threshold autoregressive models. J. Econ. 127(2), 201–224 (2005)
Inclan, C.: Detection of multiple changes of variance using posterior odds. J. Bus. Econ. Stat. 11(3), 289–300 (1993)
Li, D., Li, W.K., Ling, S.: On the least squares estimation of threshold autoregressive moving-average models. Stat. Interface 4, 183–196 (2011)
Liu, W., Ling, S., Shao, Q.M.: On non-stationary threshold autoregressive models. Bernoulli 17(3), 969–986 (2011)
Meligkotsidou, L., Tzavalis, E., Vrontos, I.D.: A Bayesian analysis of unit roots and structural breaks in the level, trend, and error variance of autoregressive models of economic series. Econ. Rev. 30(2), 208–249 (2011)
Nelson, C.R., Plosser, C.R.: Trends and random walks in macroeconmic time series: some evidence and implications. J. Monetary Econ. 10(2), 139–162 (1982)
Pan, J., Xia, Q., Liu, J.: Bayesian analysis of multiple thresholds autoregressive model. Comput. Stat. 32(1), 219–237 (2017)
So, M.K., Chen, C.W., Chen, M.T.: A Bayesian threshold nonlinearity test for financial time series. J. Forecast. 24(1), 61–75 (2005)
Tong, H.: Threshold models in non-linear time series analysis. Lect. Notes Stat. 21 (1983)
Tong, H.: Threshold models in non-linear time series analysis, vol. 21. Springer, New York (2012)
Wang, J., Zivot, E.: A Bayesian time series model of multiple structural changes in level, trend, and variance. J. Bus. Econ. Stat. 18(3), 374–386 (2000)
Watson, M.W.: Univariate detrending methods with stochastic trends. J. Monetary Econ. 18(1), 49–75 (1986)
Xia, Q., Liu, J., Pan, J., Liang, R.: Bayesian analysis of two-regime threshold autoregressive moving average model with exogenous inputs. Commun. Stat. Theory Methods 41(6), 1089–1104 (2012)
Yau, C.Y., Tang, C.M., Lee, T.C.: Estimation of multiple-regime threshold autoregressive models with structural breaks. J. Am. Stat. Assoc. 110(511), 1175–1186 (2015)
Yu, P.: Likelihood estimation and inference in threshold regression. J. Econ. 167(1), 274–294 (2012)
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Agiwal, V., Kumar, J. Bayesian estimation for threshold autoregressive model with multiple structural breaks. METRON 78, 361–382 (2020). https://doi.org/10.1007/s40300-020-00188-0
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DOI: https://doi.org/10.1007/s40300-020-00188-0