Long Run Estimations for the Volatility of Time Series in the Brazilian Financial Market

The models of the GARCH family, normally used for the estimates of volatility for longer periods, keep unchanged the relative weights assigned to the observations both old and new, regardless of the volatility´s forecasted horizon. The purpose of this article is to verify if the increase in relative weights assigned to the earlier observations due to the increase of the forecast horizon results in better estimates of volatility. Through the use of seven forecasting models of volatility and return series of financial markets assets, the estimates obtained in the sample (in-sample) were compared with observations outside the sample (out-of-sample). Based on this comparison, it was found that the best estimates of expected volatility were obtained by the modified EGARCH model and the ARLS model. We conclude that the use of traditional forecasting models of volatility, which keep unchanged relative weights assigned to both old and new observations, was inappropriate.