Discrete variable stochastic approximation procedures and recursive autoregressive model identification

Two stochastic approximation procedures are proposed for finding a point attaining the maximum of a regression function defined and observable only at points on a set of discrete variables. The asymptotic convergence property of the procedures is discussed using the theorem of almost supermartingales. The procedures are applied to the recursive identification of autoregressive time series models. The identification procedure consists of a recursive order estimation stage and a recursive autoregressive parameter updating stage, and gives the true autoregressive model or the best autoregressive approximation model.