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On hysteretic vector autoregressive model with applications. (English) Zbl 07193720

Summary: This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-\(t\) distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.

MSC:

62F15 Bayesian inference
37M10 Time series analysis of dynamical systems
62P20 Applications of statistics to economics

Software:

MVN
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Full Text: DOI

References:

[1] Tong H. On a threshold model. In: Chen CH, editor. Pattern recognition and signal processing. Amsterdam: Sijhoff and Noordhoff; 1978. [Google Scholar]
[2] Tong H, Lim KS.Threshold autoregression, limit cycles and cyclical data (with discussion). J R Stat Soc Ser B. 1980;42:245-192. [Google Scholar] · Zbl 0473.62081
[3] Tong H. Nonlinear time series: a dynamical system approach. Oxford: Oxford University Press; 1990. [Google Scholar] · Zbl 0716.62085
[4] Chan KS, Tong H.On estimating thresholds in autoregressive models. J Time Ser Anal. 1986;7:179-190. doi: 10.1111/j.1467-9892.1986.tb00501.x[Crossref], [Google Scholar] · Zbl 0596.62085
[5] Granger CWJ, Teräsvirta T. Modelling nonlinear economic relationships. Oxford: Oxford University Press; 1993. [Google Scholar] · Zbl 0893.90030
[6] Teräsvirta T.Specification, estimation, and evaluation of smooth transition autoregressive models. J Am Stat Assoc. 1994;89:208-218. [Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1254.91686
[7] Li GD, Guan B, Li WK, et al. Hysteretic autoregressive time series models. Biometrika. 2015;102:717-723. doi: 10.1093/biomet/asv017[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1452.62658
[8] Zhu K, Yu PLH, Li WK.Testing for the buffered autoregressive processes. Stat Sin. 2014;24:971-984. [Web of Science ®], [Google Scholar] · Zbl 1285.62113
[9] Chen CWS, Truong BC.On double hysteretic heteroskedastic model. J Stat Comput Simul. 2016;86:2684-2705. doi: 10.1080/00949655.2015.1123262[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1510.62355
[10] Hansen BE.Autoregressive conditional density estimation. Int Econ Rev (Philadelphia). 1994;35:705-730. doi: 10.2307/2527081[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0807.62090
[11] Zhu K, Li WK, Yu PLH.Buffered autoregressive models with conditional heteroskedasticity: an application to exchange rates. J Bus Econ Stat. 2017;35:528-542. doi: 10.1080/07350015.2015.1123634[Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[12] Jondeau E, Poon S, Rockinger M. Financial modeling under non-gaussian distributions. London: Springer-Verlag; 2007. [Google Scholar] · Zbl 1138.91002
[13] Koop G, Poirier DJ, Tobias JL. Bayesian econometric methods. Cambridge: Cambridge University Press; 2007. [Crossref], [Google Scholar] · Zbl 1136.62087
[14] Choy STB, Chen CWS, Lin EMH.Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations. Quant Finance. 2014;14:1297-1313. doi: 10.1080/14697688.2012.683878[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1402.62249
[15] Chen CWS, Gerlach R, Lin AMH.Falling and explosive, dormant and rising markets via multiple-regime financial time series models. Appl Stoch Models Bus Ind. 2010;26:28-49. doi: 10.1002/asmb.765[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1224.91185
[16] Chen CWS, Gerlach R, Tai APJ.Testing for nonlinearity in mean and volatility for heteroskedastic models. Math Comput Simul. 2008;79:489-499. doi: 10.1016/j.matcom.2008.01.044[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1151.91699
[17] Chen CWS, So MKP, Gerlach RH.Assessing and testing for threshold nonlinearity in stock returns. Aust N Z J Stat. 2005;47:473-488. doi: 10.1111/j.1467-842X.2005.00410.x[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1127.62076
[18] Li WK, McLeod AI.Distribution of the residual autocorrelations in multivariate ARMA time series models. J R Stat Soc Ser B. 1981;43:231-239. [Google Scholar] · Zbl 0505.62079
[19] Chen CWS, So MKP.On a threshold heteroscedastic model. Int J Forecast. 2006;22:73-89. doi: 10.1016/j.ijforecast.2005.08.001[Crossref], [Web of Science ®], [Google Scholar]
[20] Jones MC.A dependent bivariate t distribution with marginal on different degrees of freedom. Stat Probab Lett. 2002;56:163-170. doi: 10.1016/S0167-7152(01)00180-8[Crossref], [Web of Science ®], [Google Scholar] · Zbl 0994.62050
[21] Shaw WT, Lee KTA.Bivariate Student t distributions with variable marginal degrees of freedom and independence. J Multivar Anal. 2008;99:1276-1287. doi: 10.1016/j.jmva.2007.08.006[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1216.62081
[22] Chen CWS, Gerlach R, Liu FC.Detection of structural breaks in a time-varying heteroskedastic regression model. J Stat Plan Inference. 2011;141:3367-3381. doi: 10.1016/j.jspi.2011.05.014[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1221.62120
[23] Truong BC, Chen CWS, So MKP.Model selection of a switching mechanism for financial time series. Appl Stoch Models Bus Ind. 2016;32:836-851. doi: 10.1002/asmb.2205[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1411.62309
[24] Granger CWJ.Investigating causal relations by econometric models and cross spectral methods. Econometrica. 1969;37:424-438. doi: 10.2307/1912791[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1366.91115
[25] Berger JO, Delampady M.Testing precise hypotheses. Stat Sci. 1987;2:317-335. doi: 10.1214/ss/1177013238[Crossref], [Google Scholar] · Zbl 0955.62545
[26] Korkmaz S, Goksuluk D, Zararsiz G. MVN: Multivariate normality tests. R package version 3.7. 2014. [Google Scholar]
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