Re: [R] Time series\optimization question not R question

From: Ravi Varadhan <rvaradhan_at_jhmi.edu>
Date: Tue, 22 May 2007 11:27:27 -0400

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.



Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan_at_jhmi.edu

Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html  



-----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.


This is not an offer (or solicitation of an offer) to buy/se...{{dropped}}



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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 22 May 2007 - 15:35:53 GMT

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