On Mixture GARCH Models: Long, Short Memory and Application in Finance

Abstract

In this work, we study the famous model of volatility; called model of conditional heteroscedastic autoregressive with mixed memory MMGARCH for modeling nonlinear time series. The MMGARCH model has two mixing components, one is a GARCH short memory and the other is GARCH long memory. the main objective of this search for finds the best model between mixtures of the models we made (long memory with long memory, short memory with short memory and short memory with long memory) Also, the existence of its stationary solution is discussed. The Monte Carlo experiments demonstrate we discovered theoretical. In addition, the empirical application of the MMGARCH model (1, 1) to the daily index DOW and NASDAQ illustrates its capabilities; we find that for the mixture between APARCH and EGARCH is superior to any other model tested because it produces the smallest errors.