Abstract
This paper proposes a Bayesian unit root test for testing a non-stationary random walk of nonlinear exponential smooth transition autoregressive process. It investigates the performance of Bayes estimators and Bayesian unit root test due to its superiority in estimation and power properties than reported in existing literature. The proposed approach is applied to the real effective exchange rates of 10 selected countries of the organization of economic co-operation and development (OECD) and the paper observe some interesting findings which demonstrate the usefulness of the model.
Acknowledgments
We are thankful to anonymous referees and the editor for valuable comments which have improved the paper. The first author, Shivam Jaiswal, is grateful to the Department of Science and Technology (DST), Government of India for their financial support (INSPIRE fellowship IF150749) to pursue his research and M. I. Bhatti acknowledge OSP leave During 2019 from La Trobe Business school which enable to complete the final version of this paper at Minhaj University, Lahore.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Chan, K. S., and H. Tong. 1986. “On Estimating Thresholds in Autoregressive Models.” Journal of Time Series Analysis 7: 179–90, https://doi.org/10.1111/j.1467-9892.1986.tb00501.x.Search in Google Scholar
Chaturvedi, A., S. Gupta, and M. I. Bhatti. 2012. “Confidence Ellipsoids Based on a General Family of Shrinkage Estimators for a Linear Model with Non-spherical Disturbances.” Journal of Multivariate Analysis 104 (1): 140–58, https://doi.org/10.1016/j.jmva.2011.07.005.Search in Google Scholar
Chib, S. 1995. “Marginal Likelihood from the Gibbs Output.” Journal of the American Statistical Association 90 (432): 1313–21, https://doi.org/10.1080/01621459.1995.10476635.Search in Google Scholar
Deschamps, P. J. 2008. “Comparing Smooth Transition and Markov Switching Autoregressive Models of US Unemployment.” Journal of Applied Econometrics 23: 435–62, https://doi.org/10.1002/jae.1014.Search in Google Scholar
Geweke, J. 2007. “Bayesian Model Comparison and Validation.” American Economic Review 97 (2): 60–4, https://doi.org/10.1257/aer.97.2.60.Search in Google Scholar
Güriş, B. 2018. A Flexible Fourier Form Nonlinear Unit Root Test Based on ESTAR Model, Munich Personal RePEc Archive, 83472. Istanbul University.Search in Google Scholar
Hamilton, J. D. 1989. “A New Approach to the Economic Analysis of Nonstationary Time Series and Business Cycle.” Econometrica 57 (2): 357–84, https://doi.org/10.2307/1912559.Search in Google Scholar
Harvey, D. I., S. J. Leybourne, and E. J. Whitehouse. 2017. “Testing for a Unit Root against ESTAR Stationarity.” Studies in Nonlinear Dynamics & Econometrics 22 (1): 1–29.10.1515/snde-2016-0076Search in Google Scholar
He, C., and R. Sandberg. 2006. “Dickey-fuller Type of Tests against Non-linear Dynamic Models.” Oxford Bulletin of Economics & Statistics 68 (1): 835–86, https://doi.org/10.1111/j.1468-0084.2006.00459.x.Search in Google Scholar
Hu, J., and Z. Chen. 2016. “A Unit Root Test against Globally Stationary ESTAR Models when Local Condition Is Non-stationary.” Economics Letters 146: 89–94, https://doi.org/10.1016/j.econlet.2016.07.002.Search in Google Scholar
Li, Y., and G. Shukur. 2010. “Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion.” Communications in Statistics: Simulation and Computation 39: 277–86, https://doi.org/10.1080/03610910903443964.Search in Google Scholar
Livingston, G.Jr., and D. Nur. 2017. “Bayesian Inference for Smooth Transition Autoregressive (STAR) Model: A Prior Sensitivity Analysis.” Communications in Statistics: Simulation and Computation 46 (7): 5440–61, https://doi.org/10.1080/03610918.2016.1161794.Search in Google Scholar
Manzur, M. 2018. “Exchange Rate Economics is Always and Everywhere Controversial.” Applied Economics 50 (3): 216–32, https://doi.org/10.1080/00036846.2017.1313960.Search in Google Scholar
Peguin-Feissolle, A. 1994. “Bayesian Estimation and Forecasting in Non-linear Models’ Application to an LSTAR Model.” Economics Letters 46 (3): 187–94, https://doi.org/10.1016/0165-1765(94)00478-1.Search in Google Scholar
Shrivastava, A., A. Chaturvedi, and M. I. Bhatti. 2019. “Robust Bayesian Analysis of a Multivariate Dynamic Model.” Physica A: Statistical Mechanics and its Applications 528: 121451, https://doi.org/10.1016/j.physa.2019.121451.Search in Google Scholar
Sturtz, S., U. Ligges, and A. Gelman. 2005. “R2WinBUGS: A Package for Running WinBUGS from R.” Journal of Statistical Software 12 (3): 1–16, https://doi.org/10.18637/jss.v012.i03.Search in Google Scholar
Teräsvirta, T. 1994. “Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models.” Journal of the American Statistical Association 89: 208–18, https://doi.org/10.2307/2291217.Search in Google Scholar
Tong, H. 1978. “On a Threshold Model.” In Pattern Recognition and Signal Processing, NATO Science Series E, Vol. 29, edited by C. H. Chen, 575–86. Netherlands: Sijthoff & Noordhoff.10.1007/978-94-009-9941-1_24Search in Google Scholar
Van Dijk, D., T. Teräsvirta, and P. H. Franses. 2002. “Smooth Transition Autoregressive Models – a Survey of Recent Developments.” Econometric Reviews 21: 1–47, https://doi.org/10.1081/etc-120008723.Search in Google Scholar
Wang, S., and J. Yu. 2017. “A New Unit Root Test Based on F-Statistic in ESTAR Framework.” Applied Economics Letters 24 (19): 1412–16, https://doi.org/10.1080/13504851.2017.1282135.Search in Google Scholar
Wang, B., Q. Zhang, and W. Xie. 2019. “Bayesian Sequential Data Collection for Stochastic Simulation Calibration.” European Journal of Operational Research 277 (1): 300–16, https://doi.org/10.1016/j.ejor.2019.01.073.Search in Google Scholar
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