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

Tue May 22 17:36:54 CEST 2007

In my previous email, I meant to say:

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

So that the model becomes:

z_t = tanh(P2)*z_t-1 + epsilon_t - P1*epsilon_t-1

Although I am not sure, how readily the likelihood of the above model can be
maximized.

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

Fax: (410) 614-9625

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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 Ravi Varadhan
Sent: Tuesday, May 22, 2007 11:27 AM
To: 'Leeds, Mark (IED)'; r-help at stat.math.ethz.ch
Subject: Re: [R] Time series\optimization question not R question

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.

----------------------------------------------------------------------------
-------

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

----------------------------------------------------------------------------
--------

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

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