Estudio del efecto de apalancamiento en series financieras usando un modelo TAR
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Esta investigación demuestra que bajo ciertas condiciones matemáticas, un modelo autorregresivo de umbrales (TAR) puede representar el efecto de apalancamiento, a partir de su función de varianza condicional. Asimismo, se obtienen las expresiones analíticas para el tercer y cuarto momento del modelo TAR cuando este es débilmente estacionario, descubriendo en estos resultados importantes interpretaciones. Se realiza una ilustración empírica donde se ajustan modelos TAR a partir de la metodología de Nieto (2005) y modelos VAR-GARCH multivariados a través de la aproximación A-BEKK, para los índices bursátiles de Brasil, Colombia y Japón. Finalmente, se comparan ambos modelos estadísticos vía momentos condicionales y no condicionales, así como por la representación del efecto de apalancamiento.
Abstract. This research shows that under certain mathematical conditions, a threshold autoregressive model (TAR) can represent the leverage effect based on its conditional variance function. Furthermore, the analytical expressions for the third and fourth moment of the TAR model are obtained when it is weakly stationary. This dissertation makes an empirical application, where TAR models are fitted using Nieto’s (2005) methodology and VAR-GARCH multivariate models are estimated through A-BEKK approach to the stock indexes in Brazil, Colombia and Japan. Finally, both statistical models are compared, via conditional and unconditional moments, and the representation of the leverage effect.
Abstract. This research shows that under certain mathematical conditions, a threshold autoregressive model (TAR) can represent the leverage effect based on its conditional variance function. Furthermore, the analytical expressions for the third and fourth moment of the TAR model are obtained when it is weakly stationary. This dissertation makes an empirical application, where TAR models are fitted using Nieto’s (2005) methodology and VAR-GARCH multivariate models are estimated through A-BEKK approach to the stock indexes in Brazil, Colombia and Japan. Finally, both statistical models are compared, via conditional and unconditional moments, and the representation of the leverage effect.