Modelamiento de procesos autorregresivos de umbrales estacionales
Autores
González Borja, Joaquín
Director
Tipo de contenido
Trabajo de grado - Doctorado
Idioma del documento
EspañolFecha de publicación
2019-06-28
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Resumen
Fluctuaciones estacionales frecuentemente se hallan en muchas series de tiempo. En adición, la no linealidad y la relación con otras series de tiempo son comportamientos prominentes de muchas de tales series. En este trabajo, consideramos 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 modelada a ser estocástica y dependiente del régimen. El modelo propuesto es un caso especial de un proceso autorregresivo de umbrales con entrada exógena (TARX). Desarrollamos un procedimiento basado en métodos Bayesianos para identificar el modelo, estimar parámetros, validar el modelo y calcular pronósticos. En la etapa de identificación del modelo, presentamos una prueba estadística de estacionalidad multiplicativa por regímenes. La metodología propuesta es ilustrada con un ejemplo simulado y aplicada a datos empíricos económicos.
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 ilustrated with a simulated example and applied to economic empirical data.
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 ilustrated with a simulated example and applied to economic empirical data.