|Date: ||Wed, 5 Aug 1998 16:30:59 -0500|
|Reply-To: ||"Nichols, David" <nichols@SPSS.COM>|
|Sender: ||"SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>|
|From: ||"Nichols, David" <nichols@SPSS.COM>|
|Subject: ||Re: definition of time series terms....|
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),
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.
Principal Support Statistician and
Manager of Statistical Support
From: Dale Glaser[SMTP:dale.glaser@SHARP.COM]
Sent: Monday, August 03, 1998 2:25 PM
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?
Dale Glaser, Ph.D.
Clinical Outcomes Research/SDSU
Sharp HealthCare/Psych. Dept
San Diego, CA