Published
Forecasting with Multivariate Threshold Autoregressive Models
Pronósticos con modelos multivariados autorregresivos de umbrales
DOI:
https://doi.org/10.15446/rce.v44n2.91356Keywords:
Bayesian Approach, Forecasting, Predictive distributions, Cov- erage Percentages, Multivariate threshold autoregressive model (en)Enfoque Bayesiano, Pronóstico, Distribciones Predictivas, Porcentajes de Cobertura, Modelo Multivariado Autoregresivo de Umbrales (es)
Downloads
An important stage in the analysis of time series is the forecasting. How- ever, the forecasting in non-linear time series models is not straightforward as in linear time series models because an exact analytical of the conditional expectation is not easy to obtain. Therefore, a strategy of forecasting with multivariate threshold autoregressive(MTAR) models is proposed via predictive distributions through Bayesian approach. This strategy gives us the forecast for the response and exogenous vectors. The coverage percentages of the forecast intervals and the variability of the predictive distributions are analysed in this work. An application to Hydrology is presented.
Una etapa importante en el análisis de series de tiempo es el pronóstico. Sin embargo, el pronóstico en modelos de series de tiempo no lineales no es directo como en el caso de modelos lineales de series de tiempo porque obtener la forma exacta de la esperanza condicional no es fácil. Por lo tanto, una estrategia de pronóstico con modelos multivariados autoregresivos de umbrales(MTAR) es propuesta vía las distribuciones predictivas usando el enfoque Bayesiano. Esta esttrategia nos entrega tanto el pronóstico del vector de respuesta, como el de las variables exógenas. Los porcentajes de cobertura de los intervalos de pronóstico y la variabilidad de las distribuciones predictivas son analizadas en este trabajo. Una aplicación a la hidrología es presentada.
References
Calderon, S. & Nieto, F. (2017), ‘Bayesian analysis of Multivariate Threshold Autoregressive Models with Missing Data’, Communications in Statistics: Theory and Methods 46(1), 296–318.
De Gooijer, J. G. & Vidiella-i Anguera, A. (2004), ‘Forecasting threshold cointegrated systems’, International Journal of Forecasting 20(2), 237–253.
Dellaportas, P., Forster, J. & Ntzoufras, I. (2002), ‘On Bayesian model and variable selection using MCMC’, Statistics and Computing 12(1), 27–36.
Geweke, J. & Amisano, G. (2010), ‘Comparing and evaluating Bayesian predictive distributions of asset returns’, International Journal of Forecasting 26(2), 216–230.
Harvey, A. (1989), Forecasting, structural time series model and the Kalman filter, Cambridge University Press, Cambridge.
Kock, A. B. & Teräsvirta, T. (2011), Forecasting With Nonlinear Time Series Models, in M. P. Clements & D. F. Hendry, eds, ‘The Oxford Handbook of Economic Forecasting’, Oxford University Press, Oxford, chapter 2, pp. 61–87.
Kwon, Y. (2003), Bayesian Analysis of Threshold Autoregressive Models, PhD thesis, University of Tennessee - Knoxville.
Kwon, Y., Bozdogan, H. & Bensmail, H. (2009), ‘Performance of Model Selection Criteria in Bayesian Threshold VAR (TVAR) Models’, Econometric Reviews 28(1-3), 83–101.
Meyn, S. & Tweedie, R. (2009), Markov Chains and Stochastic Stability, Oxford Statistical Science, Cambridge University Press, Cambridge.
Nieto, F. (2005), ‘Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data’, Communications in Statistics - Theory and Methods. 34(4), 905–930.
Nieto, F. (2008), ‘Forecasting with univariate TAR models’, Statistical Methodology 5(3), 263–273.
Tong, H. (2015), ‘Threshold models in time series analysis-Some reflections’, Journal of Econometrics 189(3), 485–491.
Tsay, R. S. (1998), ‘Testing and Modeling Multivariate Threshold Models’, Journal of the American Statistical Association 93(443), 467–482.
Tsay, R, S. & Chen, R. (2018), Nonlinear Time Series Analysis, Wiley Series in Probability and Statistics, John Wiley and Sons.
Vargas, L. (2012), Cálculo de la distribución predictiva en un modelo TAR, Master’s thesis, Universidad Nacional de Colombia, Colombia.
Wu, C. & Lee, J. (2011), ‘Forecasting Time-Varying Covariance with a Robust Bayesian Threshold Model’, Journal of Forecasting 30(5), 451–468.
Dimensions
PlumX
Article abstract page views
Downloads
How to Cite
License
Copyright (c) 2021 Revista Colombiana de Estadística
This work is licensed under a Creative Commons Attribution 4.0 International License.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
