Estimating the generalized autoregression model parameters for unknown noise distribution

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.