A Novel Algorithm for GARCH Model Estimation

Abstract

Generalized autoregressive conditional heteroskedasticity (GARCH) is a popular model to describe the time-varying conditional volatility of a time series, which is widely used in signal processing and machine learning. In this paper, we focus on the model parameter estimation of GARCH based on the Gaussian maximum likelihood estimation method. Due to the recursively coupling nature of parameters in GARCH, the optimization problem is highly non-convex. In this paper, we propose a novel algorithm based on the block majorization-minimization algorithmic framework, which can take care of the per-block variable structures for efficient problem solving. Numerical experiments demonstrate that the proposed algorithm can achieve comparable and even better performance in terms of parameter estimation errors. More importantly, estimated parameters from our algorithm always guarantee a stationary model, which is a desirable property in time series volatility modeling.