Exact ARMA lattice predictors from autocorrelation functions

The paper derives an optimal linear L²-predictor of ARMA-type in the lattice form of arbitrarily fixed dimensions for a process whose autocorrelation function is known. The algorithm preserves exact optimality at each step, as opposed to asymptotic convergence of more usual algorithms, at the expense of hereditary computation. Only the discrete-time case is examined. It is shown how the unnormalized (respectively normalized) lattice form may be reduced to only 4n-2 parameters (respectively 2n+1) for a nth-order projection on the past. The normalization algorithm for the forward and backward residuals uses only scalar square root computations. Some examples that show the accuracy of this technique compared with those using the classical ARMA form for the predictor, are given