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Revista Colombiana de Estadística
versión impresa ISSN 0120-1751
Rev.Colomb.Estad. vol.43 no.2 Bogotá jul./dic. 2020 Epub 05-Dic-2020
https://doi.org/10.15446/rce.v43n2.81261
Original articles of research
Bayesian Analysis of Multiplicative Seasonal Threshold Autoregressive Processes
Análisis Bayesiano de procesos autorregresivos de umbrales estacionales multiplicativos
1 Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad del Tolima, Ibagué, Colombia
2Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá, Colombia
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.
Key words: Bayesian analysis; Exogenous variable; Multiplicative model; Nonlinearity; Seasonality; Threshold autoregressive models
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.
Palabras clave: Análisis bayesiano; Estacionalidad; Modelos autorregre-sivos de umbrales; Modelo multiplicativo; No linealidad; Variable exógena
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Received: July 2019; Accepted: January 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
