This research presents a theoretical review of the structure and applica-tion of long memory nature models that combine characteristics of the fractionally integrated processes with the classic GARCH models, thus obtaining the autoregres-sive models with fractionally integrated conditioned heterocedasticity (FIGARCH) which Through the cumulative response impulse function, I can quantify the degree of persistence of the impact of innovation on the function of conditioned variance, that is, the element of persistence in a chaotic series very sensitive to changes in initial conditions associated with fractional Brownian motion. For this application, the exchange rate variable was used, and by means of long memory time series mo-dels, the persistence of the existing effect on the volatility of said series could be analyzed.

This research presents a theoretical review of the structure and applica-tion of long memory nature models that combine characteristics of the fractionally integrated processes with the classic GARCH models, thus obtaining the autoregres-sive models with fractionally integrated conditioned heterocedasticity (FIGARCH) which Through the cumulative response impulse function, I can quantify the degree of persistence of the impact of innovation on the function of conditioned variance, that is, the element of persistence in a chaotic series very sensitive to changes in initial conditions associated with fractional Brownian motion. For this application, the exchange rate variable was used, and by means of long memory time series mo-dels, the persistence of the existing effect on the volatility of said series could be analyzed.

En este estudio, investigamos la dependencia de largo plazo o de larga memoria presente en la volatilidad de los rendimientos del mercado de valores de Perú, Brasil, México, Chile, Argentina, y el S&P500. En un primer momento se analiza el comportamiento de la ACF y la densidad espectral. Por otra parte, la volatilidad se modela por medio de procesos FIGARCH que añaden evidencia a lo observado visualmente. Para verificar la presencia de la verdadera larga memoria seguimos un enfoque de pruebas estadísticas. En este sentido, el estadístico W de Qu (2011), los estadísticos Wc, __ y Zt propuestos por Shimotsu (2006), y los estadísticos td(1=2; 1; 4=5; 1), y mean td de Perron y Qu (2010) son utilizados. También mostramos evidencia sobre el comportamiento del estimador de larga memoria b d para diferentes tamaños de las muestras incluidas en el procedimiento de estimación. La eviden...