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Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes
Análisis Bayesiano de procesos autorregresivos de umbrales estacionales multiplicativos
DOI:
https://doi.org/10.15446/rce.v43n2.81261Keywords:
Bayesian analysis, Exogenous variable, Multiplicative model, Nonlinearity, Seasonality, Threshold autoregressive models (en)Análisis bayesiano, Estacionalidad, Modelos autorregre- sivos de umbrales, Modelo multiplicativo, No linealidad, Variable exógena (es)
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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.
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 con- sidera 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.
References
Calderón, S. A. & Nieto, F. H. (2017), Bayesian analysis of multivariate threshold autoregressive models with missing data, Communications in Statistics- Theory and Methods 46(1), 296–318.
Chen, C. W. (1998), A bayesian analysis of generalized threshold autoregressive models, Statistics & Probability Letters 40(1), 15–22.
Chen, C. W., Gerlach, R. H. & Lin, A. M. (2010), Falling and explosive, dormant, and rising markets via multiple-regime financial time series models, Applied Stochastic Models in Business and Industry 26(1), 28–49.
Chen, C. W. & Lee, J. C. (1995), Bayesian inference of threshold autoregressive models, Journal of Time Series Analysis 16(5), 483–492.
Chen, C. W., Liu, F. C. & So, M. K. (2011), A review of threshold time series models in finance, Statistics and its Interface 4(2), 167–181.
Chen, C. W. & So, M. K. (2006), On a threshold heteroscedastic model, International Journal of Forecasting 22(1), 73–89.
Congdon, P. (2006), Bayesian model choice based on monte carlo estimates of posterior model probabilities, Computational Statistics & Data Analysis
(2), 346–357.
Congdon, P. (2007), Bayesian statistical model ling, Vol. 704, 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 and Economics 32(1), 3–18.
Dellaportas, P., Forster, J. J. & Ntzoufras, I. (2002), On bayesian model and variable selection using mcmc, Statistics and Computing 12(1), 27–36.
Di Narzo, A. F. & Di Narzo, F. (2013), Tserieschaos: Analysis of nonlinear time series. R package version 0.1-13.
Dickey, J. M. (1971), The weighted likelihood ratio, linear hypotheses on normal location parameters, The Annals of Mathematical Statistics 42(1), 204–223.
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 production, International Journal of Forecasting 21(1), 87–102.
Gelfand, A. E. & Smith, A. F. (1990), Sampling-based approaches to calculating marginal densities, Journal of the American Statistical Association 85(410), 398–409.
George, E. I. & McCulloch, R. E. (1993), Variable selection via gibbs sampling, Journal of the American Statistical Association 88(423), 881–889.
Gerlach, R., Carter, C. & Kohn, R. (1999), Diagnostics for time series analysis, Journal of Time Series Analysis 20(3), 309–330.
Gerlach, R. & Chen, C. W. (2008), Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models, Statistics and Computing 18, 391–408.
Geweke, J. (1992), Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments, In Bayesian Statistics 4, Oxford University Press, Oxford.
González, J. (2019), Modelamiento de procesos autorregresivos de umbrales estacionales, PhD thesis, Disertación doctoral en ciencias estadísticas, Universidad Nacional de Colombia, Bogotá.
Hansen, B. E. (2011), Threshold autoregression in economics, Statistics and its Interface 4(2), 123–127.
Kass, R. E. & Raftery, A. E. (1995), Bayes factors, Journal of the American Statistical Association 90(430), 773–795.
Kuo, L. & Mallick, B. (1998), Variable selection for regression models, Sankhy¯a: The Indian Journal of Statistics, Series B 60(1), 65–81.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N. & Teller, A. H. (1953), Equation of state calculations by fast computing machines, The Journal of Chemical Physics 21(6), 1087–1092.
Meyn, S. P. & Tweedie, R. L. (2009), Markov chains and stochastic stability, 2 edn, Springer Science & Business Media, New York.
Nieto, F. H. (2005), Modeling bivariate threshold autoregressive processes in the presence of missing data, Communications in Statistics. Theory and Methods 34, 905–930.
Nieto, F. H. (2008), Forecasting with univariate tar models, Statistical Methodology 5(3), 263–276.
Nieto, F. H. & Moreno, E. C. (2016), Univariate conditional distributions of an open-loop tar stochastic process, Revista Colombiana de Estadística
(2), 149–165.
Nieto, F. H., Zhang, H. & Li, W. (2013), Using the reversible jump mcmc procedure for identifying and estimating univariate tar models, Communications in Statistics-Simulation and Computation 42(4), 814–840.
OHara, R. B. & Sillanpä, M. J. (2009), A review of bayesian variable selection methods: what, how and which, Bayesian Analysis 4(1), 85–117.
Plummer, M., Best, N., Cowles, K. & Vines, K. (2006), CODA: convergence diagnosis and output analysis for MCMC, R news 6(1), 7–11.
So, M. K. & Chen, C. W. (2003), Subset threshold autoregression, Journal of Forecasting 22(1), 49–66.
So, M. K., Chen, C. W. & Liu, F.-C. (2006), Best subset selection of autoregressive models with exogenous variables and generalized autoregressive conditional heteroscedasticity errors, Journal of the Royal Statistical Society: Series C (Applied Statistics) 55(2), 201–224.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P. & Van Der Linde, A. (2002), Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64(4), 583–640.
Team, R. D. C. (2016), R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. *https://www.R-project.org/
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, 485–491.
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, Series B 42(3), 245–292.
Tsay, R. S. (1998), Testing and modeling multivariate threshold models, Journal of the American Statistical Association 93(443), 1188–1202.
Vaca, P. A. (2018), Analysis of the forecasting performance of the threshold autoregressive model, Masters thesis, Universidad Nacional de Colombia, Bogotá.
Vargas, L. (2012), Cálculo de la distribución predictiva en un modelo TAR, Masters thesis, Universidad Nacional de Colombia.
Verdinelli, I. & Wasserman, L. (1995), Computing bayes factors using a generalization of the savage-dickey density ratio, Journal of the American Statistical Association 90(430), 614–618.
Zhang, H. & Nieto, F. H. (2015), Tar modeling with missing data when the white noise process follows a students t-distribution, Revista Colombiana de Estadística 38(1), 239–266.
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1. Nicolás Rivera Garzón, Sergio Alejandro Calderón Villanueva, Oscar Espinosa. (2025). Forecasting based on a multivariate autoregressive threshold model (MTAR) with a multivariate Student’s t error distribution: A Bayesian approach. Communications in Statistics - Theory and Methods, , p.1. https://doi.org/10.1080/03610926.2025.2466738.
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