Time series: theory and methods
Time series: theory and methods
On Sequential Parameter Estimation Problem of Nonlinear Discrete-Time Stochastic Systems
ICICIC '08 Proceedings of the 2008 3rd International Conference on Innovative Computing Information and Control
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We solve the problem of estimating the autoregressive parameters of a nonlinear stable stochastic process with discrete time of the AR(p)/ARCH(p) type with unknown ARCH(p) process parameters. For the AR(1)/ARCH(1) model, we solve the estimation problem for all unknown process parameters, i.e., the autoregression parameter and two parameters of the noise process ARCH(1). We assume that the noise distributions are unknown. We show that the least square estimates are strongly consistent.