Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes

• Autores: Joaquín González, Fabio H. Nieto
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 43, Nº. 2, 2020, págs. 251-285
• Idioma: inglés
• DOI: 10.15446/rce.v43n2.81261
• Títulos paralelos:
  • Análisis Bayesiano de procesos autorregresivos de umbrales estacionales multiplicativos
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Las fluctuaciones estacionales son frecuentes en series de tiempo. En adición, la no linealidad y la relación con otras series de tiempo son comportamientos prominentes de muchas series. En este artículo, se considera el modelamiento de procesos autorregresivos de umbrales estacionales multiplicativos con entrada exógena (TSARX), los cuales incorporan en forma explícita y simultánea estacionalidad multiplicativa y no linealidad de umbrales. La estacionalidad es estocástica y dependiente del régimen. Se desarrolla un procedimiento basado en métodos Bayesianos para identificar el modelo, estimar sus parámetros, validarlo y calcular pronósticos. En la etapa de identificación del modelo, se presenta una prueba estadística de estacionalidad multiplicativa por regímenes. La metodología propuesta es ilustrada con un ejemplo simulado y aplicada a datos empíricos económicos.

  • English

    Abstract Seasonal fluctuations are often found in many time series. In addition, non-linearity and the relationship with other time series are prominent behaviors of several, of such series. In this paper, we consider the modeling of multiplicative seasonal threshold autoregressive processes with exogenous input (TSARX), which explicitly and simultaneously incorporate multiplicative seasonality and threshold nonlinearity. Seasonality is modeled to be stochastic and regime dependent. The proposed model is a special case of a threshold autoregressive process with exogenous input (TARX). We develop a procedure based on Bayesian methods to identify the model, estimate parameters, validate the model and calculate forecasts. In the identification stage of the model, we present a statistical test of regime dependent multiplicative seasonality. The proposed methodology is illustrated with a simulated example and applied to economic empirical data.

• Referencias bibliográficas
  • Calderón, S. A.,Nieto, F. H.. (2017). 'Bayesian analysis of multivariate threshold autoregressive models with missing data'. Communications...
  • Chen, C. W.. (1998). 'A bayesian analysis of generalized threshold autoregressive models'. Statistics & Probability Letters. 40....
  • Chen, C. W.,Gerlach, R. H.,Lin, A. M.. (2010). 'Falling and explosive, dormant, and rising markets via multiple-regime financial time...
  • Chen, C. W.,Lee, J. C.. (1995). 'Bayesian inference of threshold autoregressive models'. Journal of Time Series Analysis. 16. 483
  • Chen, C. W.,Liu, F. C.,So, M. K.. (2011). 'A review of threshold time series models in finance'. Statistics and its Interface. 4....
  • Chen, C. W.,So, M. K.. (2006). 'On a threshold heteroscedastic model'. International Journal of Forecasting. 22. 73-89
  • Congdon, P.. (2006). 'Bayesian model choice based on monte carlo estimates of posterior model probabilities'. Computational Statistics...
  • Congdon, P.. (2007). Bayesian statistical modellin. John Wiley & Sons, Southern Gate. Chichester.
  • Crespo, J.. (2001). Modelling seasonal asymmetries using seasonal setar models. Working Paper.
  • De Gooijer, J. G.,Vidiella-i Anguera, A.. (2003). 'Nonlinear stochastic inflation modelling using seasetars'. Insurance: Mathematics...
  • Dellaportas, P.,Forster, J. J.,Ntzoufras, I.. (2002). 'On bayesian model and variable selection using mcmc'. Statistics and Computing....
  • Di Narzo, A. F.,Di Narzo, F.. (2013). 'Tserieschaos: Analysis of nonlinear time series. R package.
  • Dickey, J. M.. (1971). 'The weighted likelihood ratio, linear hypotheses on normal location parameters'. The Annals of Mathematical...
  • Franses, P. H.,de Bruin, P.,van Dijk, D.. (2000). Seasonal smooth transition autoregression, Technical report. Erasmus University. Amsterdam....
  • Franses, P. H.,Van Dijk, D.. (2000). Non-linear time series models in empirical finance,. Cambridge University Press. Cambridge.
  • Franses, P. H.,Van Dijk, D.. (2005). 'The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial...
  • Gelfand, A. E.,Smith, A. F.. (1990). 'Sampling-based approaches to calculating marginal densities'. Journal of the American Statistical...
  • George, E. I.,McCulloch, R. E.. (1993). 'Variable selection via gibbs sampling'. Journal of the American Statistical Association....
  • Gerlach, R.,Carter, C.,Kohn, R.. (1999). 'Diagnostics for time series analysis'. Journal of Time Series Analysis. 20. 309
  • Gerlach, R.,Chen, C. W.. (2008). 'Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models'....
  • Geweke, J.. (1992). Bayesian Statistics 4. Oxford University Press. Oxford.
  • González, J.. (2019). Modelamiento de procesos autorregresivos de umbrales estacionales. Universidad Nacional de Colombia. Bogotá.
  • Hansen, B. E.. (2011). 'Threshold autoregression in economics'. Statistics and its Interface. 4. 123
  • Kass, R. E.,Raftery, A. E.. (1995). 'Bayes factors'. Journal of the American Statistical Association. 90. 773
  • Kuo, L.,Mallick, B.. (1998). 'Variable selection for regression models'. Sankhya: The Indian Journal of Statistics, Series. 60. 65-81
  • Metropolis, N.,Rosenbluth, A. W.,Rosenbluth, M. N.,Teller, A. H.. (1953). 'Equation of state calculations by fast computing machines'....
  • Meyn, S. P.,Tweedie, R. L.. (2009). Markov chains and stochastic stability. 2. Springer Science & Business Media. New York.
  • Nieto, F. H.. (2005). 'Modeling bivariate threshold autoregressive processes in the presence of missing data'. Communications in Statistics....
  • Nieto, F. H.. (2008). 'Forecasting with univariate tar models'. Statistical Methodology. 5. 263
  • Nieto, F. H.,Moreno, E. C.. (2016). 'Univariate conditional distributions of an open-loop tar stochastic process'. Revista Colombiana...
  • Nieto, F. H.,Zhang, H.,Li, W.. (2013). 'Using the reversible jump mcmc procedure for identifying and estimating univariate tar models'....
  • O'Hara, R. B.,Sillanpá, M. J.. (2009). 'A review of bayesian variable selection methods: what, how and which'. Bayesian Analysis....
  • Plummer, M.,Best, N.,Cowles, K.,Vines, K.. (2006). 'CODA: convergence diagnosis and output analysis for MCMC'. R news. 6. 7-11
  • So, M. K.,Chen, C. W.. (2003). 'Subset threshold autoregression'. Journal of Forecasting. 22. 49-66
  • So, M. K.,Chen, C. W.,Liu, F.-C.. (2006). 'Best subset selection of autoregressive models with exogenous variables and generalized autoregressive...
  • Spiegelhalter, D. J.,Best, N. G.,Carlin, B. P.,Van Der Linde, A.. (2002). 'Bayesian measures of model complexity and fit'. Journal...
  • Team, R. D. C.. (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria.
  • Tong, H.. (1990). Non-linear time series: a dynamical system approach. Oxford University Press. Oxford.
  • Tong, H.. (2015). 'Threshold models in time series analysis-some reflections'. Journal of Econometrics. 189. 485
  • Tong, H.,Chen, C. H.. (1978). Pattern recognition and signal processing. Springer Netherlands, chapter On a Threshold Model.
  • Tong, H. L.,Lim, K.. (1980). 'Threshold autoregression, limit cycles, and cyclical data'. Journal of the Royal Statistical Society,...
  • Tsay, R. S.. (1998). 'Testing and modeling multivariate threshold models'. Journal of the American Statistical Association. 93. 1188
  • Vaca, P. A.. (2018). Analysis of the forecasting performance of the threshold autoregressive model. Universidad Nacional de Colombia. Bogotá....
  • Vargas, L.. (2012). Cálculo de la distribución predictiva en un modelo TAR. Universidad Nacional de Colombia.
  • Verdinelli, I.,Wasserman, L.. (1995). 'Computing bayes factors using a generalization of the savage-dickey density ratio'. Journal...
  • Zhang, H.,Nieto, F. H.. (2015). 'Tar modeling with missing data when the white noise process follows a student's t-distribution'....