On the relationship between levinson recursion and the r and s arrays for arma model identification

Motivated by the papers of Woodward and Gray (1979) and Gray, Kelly and McIntire (1978) on the R and S array approach to ARMA modeling, the authors show that the R and S array algorithm is completely equivalent to Levinson recursion. Since entries in the R and S array can be computed by either algorithm, the equivalence provides greater insight into the R and S methodology as well as its links to Akaike's AIC or FPE. Numerical simulations serve to highlight the differences between the various approaches as well as illustrate the problems associated with exact methods. The K and S array approach is shown to be an effective procedure for determining ARMA model orders.