On Sequential Parameter Estimation Problem of Nonlinear Discrete-Time Stochastic Systems

The parameter estimation problem of partly observed nonlinear discrete-time stochastic system is considered. The unobserved component of the system is a q-dimensional stable autoregressive process of the p-th order with random parameters, observed in the presence of multiplicative and additive noises. The distributions of all the noises of the system are supposed to be unknown. In the case of Gaussian noises, autoregressive process with drifting parameters is equivalent to well-known in financial mathematics GARCH model. The problem is to estimate the mean of the drifting parameters of the object and variances of the additive noises of the system. Sequential estimators with given mean square accuracy are obtained on the basis of the correlation method.