Simultaneous parameter estimation and state smoothing of complex GARCH process in the presence of additive noise

Abstract

ARCH and GARCH models have been used recently in model-based signal processing applications, such as speech and sonar signal processing. In these applications, additive noise is often inevitable. Conventional methods for parameter estimation of ARCH and GARCH processes assume that the data are clean. The parameter estimation performance degrades greatly when the measurements are noisy. In this paper, we propose a new method for parameter estimation and state smoothing of complex GARCH processes in the presence of additive noise. Simulation results show the advantage of the proposed method in noisy environments.