Parameter Estimation for Student-t ARCH Model using MDL Criterion

In this paper the student-t autoregressive conditional heteroscedasticity (ARCH) model is considered and a new estimator for the coefficients of the ARCH model and the degree of freedom of the Student-t noise is proposed. ARCH models have been used in numerous applications to model the unpredictability and the strong dependence of the instantaneous variability of a time series on its own past. The usual approach for estimating the ARCH parameters is using QML estimator. This estimator is consistent and asymptotically efficient, but for limited data length it has poor efficiency. Simulation results show that the proposed method has better efficiency even in limited data length case. The price one should pay to obtain this performance is the increased computational load.