I'm pleased to announce that our code for exact ML estimation of ARMA models is now (in git and snapshots) MUCH faster than it used to be (like, two orders of magnitude faster in many cases). This is due to two main factors. First, we now use by default G. Melard's algorithm AS 197 (Applied Statistics, 1984). This employs a very compact recursion similar to but distinct from the Kalman filter. Second, Jack developed an elegant means of "flipping" an MA polynomial that has roots inside the unit circle: this means that our Hannan-Rissanen initializer should never be unusable, and also that BFGS has less work to do. (We never have to tell it, "You're out of bounds, try again.") One qualification: we can't use AS 197 when there are missing values within the sample range; computing the MLE in that case requires the Kalman filter. However, our first resort is now the Kalman algorithm AS 154 (Gardner, Harvey and Phillips, 1980). This is not as fast as AS 197 but, being specialized for ARMA, it's still a good deal faster than using our general-purpose Kalman code. The most difficult case is ARIMA (i.e. with differencing) in the presence of missing values: that demands an extended state-space representation incorporating levels, for which we fall back on our original Kalman code. At present there are two "secret" (undocumented) options for the arma/arima command, which we've used for testing. We could document these and make them generally available but I'm not sure that would be worthwhile. Anyway, in case anyone wishes to do some testing, here they are: First, there's an option to force use of AS 154 when AS 197 would be used by default: arma ... --as=154 Second, there's an option to use our original Kalman code when AS 197 or AS 154 would be used by default: arma ... --kalman To summarize, the default algorithm is AS 197 unless there are missing values, in which case we use AS 154 if the specification is plain ARMA or our full Kalman code if it's ARIMA. Thanks go to Oleh for pushing us in this direction! Allin