State Space Estimation for Long Memory ARFIMA-GARCH Models

This paper considers the state space representation for the ARFIMA-GARCH model, which combines both the long memory time series and the conditional heteroscedastic processes. Although this state space representation is infinite dimensional, an exact maximum likelihood (ML) estimator based on this kind of representation can be computed in a finite number of iterations. Quasi ML estimators based on the autoregressive approximation for the likelihood function are proposed. Due to the facility of the state space representation, these estimation approaches can be easily applied to the missing data case. Simulation results of both the non-missing data case and the missing data case are reported. A real data example from stock market illustrates the proposed method.