Long Memory Behavior in the Returns of the Mexican Stock Market: Arfima Models and Value at Risk Estimation

Models previously applied to the case of emerging markets have neglected to study the presence of long memory of asset returns taking into account autoregressive fractionally integrated models and different distribution alternatives. To analyze volatility and the persistence of long memory in the returns of the Mexican stock market, as well as to determine more efficient alternatives for VaR analysis, this work applies models from the ARCH family with autoregressive fractionally integrated moving average (ARFIMA) for the mean equation; these models are estimated under alternative assumptions of normal, student-t, and skewed student-t distributions of the error term. Backtestig is used to validate the efficiency of the alternative VaR estimates; these correspond to a one day ahead investment horizon. Daily returns data for the period January 1983 to December 2009 are used to carry out the corresponding econometric analysis.