# [R] Time series\optimization question not R question

Tue May 22 17:27:27 CEST 2007

Your approach obviously won't give you the same result as when the
likelihood is optimized jointly with A and \beta.  However, you can maximize
the likelihood over \beta for different values of A, which would give you a
"profiled" likelihood.  Then you pick the \beta and A corresponding to
maximum of the profiled likelihood.  However, this set of A and \beta need
not necessarily satisfy your constraints.  If this does happen, you could
make a simple parameter transformation from (A, beta) to (P1, P2) that might
resolve the problem:

P1 <- beta
P2 <- atanh(A + beta)

Ravi.

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Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Leeds, Mark (IED)
Sent: Tuesday, May 22, 2007 10:29 AM
To: r-help at stat.math.ethz.ch
Subject: [R] Time series\optimization question not R question

This is a time series\optimization rather than an R question : Suppose I
have an ARMA(1,1) with
restrictions such that the coefficient on the lagged epsilon_term is
related to the coefficient on
The lagged z term as below.

z_t =[A + beta]*z_t-1 + epsilon_t - A*epsilon_t-1

So, if I don't have a facility for optimizing with this restriction, is
it legal to set A to something and then
Optimize just for the beta given the A ? Would this give me the same
answer likelihood wise, of optimizing both
jointly with the restriction ? This methodology doesn't sound right to
me. Thanks.

P.S : abs(A + beta) also has to be less than 1  but I was just going to
hope for that and not worry about it right now.
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