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FIR-GARCH: Realizing Long Memory and Asymmetries in Returns Volatility

We introduce the class of FIR-GARCH models in this paper. FIR-GARCH models provide a parsimonious joint model for low-frequency returns and realized measures, and are sufficiently flexible to capture long memory as well as asymmetries related to leverage effects. We analyze the performances of the models in a realistic numerical study and on the basis of a dataset composed of 65 equities. Using more than 10 years of high-frequency transactions, we document significant statistical gains related to the FIR-GARCH models in terms of in-sample fit, out-of-sample fit, and forecasting accuracy compared to classical and Realized GARCH models.