The documentation for arima indicates that the stabilization of the AR parameters takes place during optimization while the MA terms are constrained afterwards. We were curious as to why that was done. How does this affect the Kalman recursion given that Jones states that both stability and invertibility are required? Is this a performance trick? Please respond directly to me as I am not a member of the list. Thanks! -joe yarmus From the R arima doc: "If transform.pars is true, the optimization is done using an alternative parametrization which is a variation on that suggested by Jones (1980) and ensures that the model is stationary. For an AR(p) model the parametrization is via the inverse tanh of the partial autocorrelations: the same procedure is applied (separately) to the AR and seasonal AR terms. The MA terms are not constrained to be invertible during optimization, but they will be converted to invertible form after optimization if transform.pars is true."