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.

The objective of the study is to compare long memory models to model exchange rate volatility. For this objective, the nominal sol / dollar exchange rate is used, covering the periods from July 19, 1999 to November 19, 2013. Essentially, it seeks to examine the prediction capacity between long memory models and hyperbolic behavior of the autocorrelations given by FIGARCH, HYGARCH and IGARCH and concluding that the FIGARCH model (1,0,637,1) using a t-student distribution has a better predictive capacity. The prediction of exchange rate volatility in the case of Peru is structurally important in the calculation of Value at Risk (VaR) and in risk management.

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.

The objective of the study is to compare long memory models to model exchange rate volatility. For this objective, the nominal sol / dollar exchange rate is used, covering the periods from July 19, 1999 to November 19, 2013. Essentially, it seeks to examine the prediction capacity between long memory models and hyperbolic behavior of the autocorrelations given by FIGARCH, HYGARCH and IGARCH and concluding that the FIGARCH model (1,0,637,1) using a t-student distribution has a better predictive capacity. The prediction of exchange rate volatility in the case of Peru is structurally important in the calculation of Value at Risk (VaR) and in risk management.

The research studies the dynamics of the volatility of the nominal exchange rate of the Peruvian nuevo sol against the US dollar, with the aim of identifying signs of dependencies over long time distances. The existence of persistence in the increases in yields and the volatility process is explored by applying two tests based on periodograms, the Hurst exponent is estimated, its consistency over time and the graphical analysis of its distributions for the subsequent application of the algorithm of complex dynamics. For this objective, the time series of the nominal exchange rate of the nuevo sol against the dollar from January 3, 2013 to February 11, 2021 is used. A nongeometric decay was identified in the correlograms in its nonlinear transformation and estimates of the fractional integration parameter d > 0 together with the empirical and rescaled Hurst estimates H > 0.5, therefore it...

Analiza el cambio de paradigma de un movimiento browniano ordinario a un movimiento browniano fraccional en el proceso de la volatilidad del tipo de cambio, es decir el elemento de persistencia en una serie caótica muy sensible a cambios en las condiciones iniciales, los cuales generan impactos decisivos en la dinámica de su movimiento de esta manera identificándose patrones en su conducta a primera vista aleatoria, pero fractalmente con un patrón a modelar, se demuestra que la serie de tiempo sujeto de estudio es un proceso con incrementos no estacionarios y dependientes distinguidas por la no linealidad negando la posibilidad de ser un proceso martingala, debido a la evidencia del coeficiente de Hurts y otras pruebas semiparamétricas que la respaldan por lo que se demuestra también que la variación cuadrática del proceso es cero. Por otro lado se muestra que dicha persistencia ...