ARCH and GARCH parameter estimation in presence of additive noise using particle methods

In this paper, we propose a new method based on particle filters for maximum likelihood (ML) estimation of the parameters of autoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH) models. Our method is based on gradient descend method and active set method for maximizing the likelihood function over parameters under stationarity constraints. The gradient of the likelihood function of observation given the parameters of the model, which is needed for gradient based optimization algorithm, is estimated using particle methods. Simulation results show the advantage of the proposed method over competing techniques.