Let y_n, n ∈Φ, be an observable random sequence generated by   where ε_n for n ∈Φ is a sequence of independent identically distributed random variables with zero mean and finite fourth-order moment.In the paper an adaptive method is considered which gives estimations   for the unknown parameters ^r and β^s and also a prediction   for y_n+1at each time n. Mean square convergence of the parameter estimations to the actual values and asymptotical optimality (in the sense of the least square error) of the prediction are proved.