Melard's algorithm is a method for obtaining maximum likelihood estimates of the models in ARMA models with complete data. Details are available from:

Melard, G. (1984). A fast algorithm for the exact likelihood of autoregressive-moving average models. Applied Statistics, 33, 104-114.

Pearlman, J. G. (1980). An algorithm for the exact likelihood of a high-order autoregressive-moving average process. Biometrika, 67(1), 232-233.

Morf, M., Sidhu, G. S., & Kailath, T. (1974). Some new algorithms for recursive estimation in constant, linear, discrete-time systems. IEEE Transactions on Automatic Control, Vol. AC-19, No. 4, 315-323.

On the Marquardt constant, in the 1976 first edition of Box and Jenkins, the algorithm described on pages 504-505 is the one (or the basis for) the algorithm used in SPSS ARIMA for solving a nonlinear least squares problem. On page 505 there is an equation that reads something like A*(sub ii)=1+pi. Pi here is lambda in SPSS ARIMA, the Marquardt constant.

David Nichols Principal Support Statistician and Manager of Statistical Support SPSS Inc.

---------- From: Dale Glaser[SMTP:dale.glaser@SHARP.COM] Sent: Monday, August 03, 1998 2:25 PM To: SPSSX-L@UGA.CC.UGA.EDU Subject: definition of time series terms....

couple of quick questions to further understand ARIMA printout:

1) "Melard's algorithm will be used for estimation" what is the nature of "Melard's algorithm" ?

2) what is the definition of "Marquardt constant"?.....I see one citation to Marquardt in Box and Jenkins (1994) in the context of finding suitable deltas with the Marquardt's 1963 paper cited in Box and Jenkins "Some problems include special features to avoid overshoot and to spped up convergence".......but I have no idea if this is even pertinent....

3) further, if the AIC for a (0 0 1) model is -663.83 and the AIC for a (0 1 1) model is -750.09 does the latter model, with a higher negative value, indicate a better fit?

thanks!

Dale Glaser, Ph.D. Clinical Outcomes Research/SDSU Sharp HealthCare/Psych. Dept San Diego, CA