Algorithm choice for (partial) autocorrelation functions

Different methods for calculating partial autocorrelation coefficients can produce different estimates, and these differences can be non-trivial. It has long been known that the Yule-Walker equations are particularly susceptible to numerical error, yet it is the most widely used method in statistical and econometric software. Two other methods, conditional maximum likelihood and Burg's algorithm are known to be more reliable, yet are infrequently used. All three methods are applied to several datasets. A forecasting example shows that a model identified by Yule-Walker can produce inferior forecasts.