STRONG CONSISTENCY OF NONLINEAR RECURSIVE ALGORITHMS OF ESTIMATION OF THE PARAMETERS OF LINEAR DIFFERENCE-EQUATIONS

Parameter estimation is considered for regression-autoregression equations with a random perturbation of sliding-mean type. The parameter estimates are constructed by a stochastic gradient algorithm with a scalar step and a nonlinear "generalized residual" transformation. Conditions are obtained for the step of the algorithm, the nonlinearity of the transformation, and the character of the external disturbances that ensure strong consistency of the estimates constructed. Examples are also presented.