Fwd: tsDyn

[Antonio, Fabio Di Narzo]

---------- Forwarded message ----------
From: Gooijer, J.G. de <J.G.de...@uva.nl>
Date: 2011/11/23
Subject: tsDyn
To: "antoni...@gmail.com" <antoni...@gmail.com>

Dear Dr. Fabio,

In a previous version of tsDyn, estimation of LSTAR models produced,
apart from parameter estimates, standard deviations and t-statistics.
In the current version, only parameter estimates are listed. Is there
any reason for this?

I noticed that estimation of SETAR models gives full estimation
results, including standard deviations, and t-statistics.

Looking forward hearing from you. Jan G. De Gooijer

--
Antonio Fabio Di Narzo, PhD.
Swiss Institute for Bioinformatics - Bioinformatics Core Facility
Office 2029, Génopode, Quartier Sorge
CH-1015 Lausanne, Switzerland
Tel: +41 21 692 4087
Fax: +41 21 692 4065

[Matthieu Stigler]

Dear Jan, Antonio and Jose

Concerning the change from version 0.5 to 0.7 that summary of lstar does not show the se/tval/pval anymore. I figured out hwat had happened: I think we changed the lstar algorithm, from estimating all the parameters with ML to the two stage approach, where slope parameters are estimated with LS conditional on transition function parameters values, and these parameters are estimated as MLE with optim(). Since we use this "conditional least square", we do not provide se estimates.

I think this can handled easily by getting the se separately, once for the transition function parameters, once for the slope ones. I worked on this and it is more or less ready, but wanted before to hear your opinion about this. What do you think? I know LSTAR less than SETAR, but in the case of SETAR we have this result that the threshold estimator being super-convergent, we can estimate and treat the slope coefs as if the threshold was known. I guess we can/should adopt the same approach for the LSTAR? Someone can confirm this?

Another way could be to re-run the "one step" approach fully with optim() with starting values the coef obtained in the "two steps" approach. I am not sure however we would not get issues with the gradient/hessian, in the (likely) case the second optimisation leads to same maximum than the first?

José, this is also the case for the star() model, where:

example(star)
summary(mod.star)

does not return se/tval/pval. Should I implement the same approach there too?

Thanks for your comments!

Mat


Le 29/11/2011 08:24, Gooijer, J.G. de a écrit :

Dear Matthieu,

 

Great! Please let me know when the new version of the tsDyn package becomes available for downloading. Thank you.

 

Regards, Jan

 

---

From: Matthieu Stigler [matthieu...@gmail.com]
Sent: Wednesday, November 23, 2011 11:01 PM
To: Gooijer, J.G. de
Cc: Antonio, Fabio Di Narzo
Subject: Re: tsDyn

Dear Mr deGooijer

I am glad to see that you are using tsDyn, I remember reading papers of you on the topic!

You are right, returning the full coefficient matrix was doable before, and now not anymore. The change was done three years ago (!) but can be re-established without problems. I will hopefully have time this week-end to work on it, so by the end of next week this should be available in tsDyn.

Best

Matthieu

2011/11/23 Antonio, Fabio Di Narzo <antoni...@gmail.com>

[Antonio, Fabio Di Narzo]

Dear all,
you might already know I'm not anymore in the time series modeling
business since a while, so I'm not able to comment specifically on
your proposed patch, matt.
What I can say, I remember taking the s.e. stuff for setar from
textbooks/papers. If there is no literature on how to get s.e. from
the lstar estimates obtained with the new method, and s.e. being
highly appreciated by users, I guess doing ML maximization after the 2
stages procedure would be a workable solution, although appropriate
notes should be added in the doc or output.

just my 2 (swiss-franc) cents,
antonio.

2011/11/30 Matthieu Stigler <matthieu...@gmail.com>:

[José Luis Aznarte]

On 11/30/11 20:04, Matthieu Stigler wrote:

Dear Jan, Antonio and Jose

Concerning the change from version 0.5 to 0.7 that summary of lstar does not show the se/tval/pval anymore. I figured out hwat had happened: I think we changed the lstar algorithm, from estimating all the parameters with ML to the two stage approach, where slope parameters are estimated with LS conditional on transition function parameters values, and these parameters are estimated as MLE with optim(). Since we use this "conditional least square", we do not provide se estimates.

I think this can handled easily by getting the se separately, once for the transition function parameters, once for the slope ones. I worked on this and it is more or less ready, but wanted before to hear your opinion about this. What do you think? I know LSTAR less than SETAR, but in the case of SETAR we have this result that the threshold estimator being super-convergent, we can estimate and treat the slope coefs as if the threshold was known. I guess we can/should adopt the same approach for the LSTAR? Someone can confirm this?

Sounds good to me, although I cannot support it theoretically.

Another way could be to re-run the "one step" approach fully with optim() with starting values the coef obtained in the "two steps" approach. I am not sure however we would not get issues with the gradient/hessian, in the (likely) case the second optimisation leads to same maximum than the first?

Sorry, Mat, I can answer this cuestion.

José, this is also the case for the star() model, where:

example(star)
summary(mod.star)

does not return se/tval/pval. Should I implement the same approach there too?

I'd say yes, go for the same modif. But again, no theoretical support from my side.

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[Matthieu Stigler]

Thanks to all of you for your answers!!

So I went a little bit into the literature, but did not find that much about this precise issue (looking in handbooks of Dick and Franses, or newest of Terasvirta Granger and Tjostheim).

First correction is that indeed (as pointed out by Jan) the estimator is NLS, not MLE. But I think in this context of normal distribution, this does not change anything?

Also, I think the estimators for SETAR and LSTAR are really different, and the result of super-convergence of SETAR does not seem to hold in the LSTAR context (I mean, I haven't seen in mentioned anywhere), as there is not this discontinuity that implies super-conv of the threshold estimator. In this regard, using the first approach I was thinking of (se from MLE and from LS in two steps) implies to impose block-diagonality in the cov matrix, which is not justified in large samples (unlike SETAR) nor desired in short sample...

So I will go on the second idea of re-estimating with a second optim(), this time with all parameters, which should give se estimates taking into account variability in all parameters.

This said, I would be interested in your benchmarks, Jan. I am surprised you find discrepancies in the estimates, and would be curious if you could share some of these results, so that we can see what explain the differences. SETAR have been benchmarked according to a paper of Hansen, was also looking for a LSTAR paper to benchmark on!

Best

Mat

2011/12/1 José Luis Aznarte <jlaz...@decsai.ugr.es>