Re: [Gretl-users] MLE of time series distribution
Oscar
Set up as a standard maximum likelihood maximisation program as in
Chapter 10 of the users guide. You can use pdf function to calculate
your likelihood or code it directly. As far as I can remember the pdf
function for the t-distribution can take non integer degrees of
freedom so your maximum likelihood estimate of the number of degrees
of freedom will almost certainly not be an integer.
Are you sure that your data have a standard t-distribution. Otherwise
you may need to make some adjustment for the mean and variance of the
data. There is an extended version of the t-distribution that allows
one to estimate a non-zero mean, nonunitary scale and degrees of
freedom using maximum likelihood. See Weitzman (2007), Subjective
expectations and asset-return puzzles, American Economic Review 97(4)
1102-1130. The required form of the pdf is given on page 126 of
http://www.tcd.ie/Economics/staff/frainj/Stable_Distribution/thesis_main_....
Best Regards
John Frain
On 25 July 2011 12:00, Oscar Soppelsa <oscar.soppelsa(a)bancaakros.it> wrote:
Hi all,
I’m reading the manual, but I don’t find how to estimate the pdf parameters
of a time series. Suppose I load in gretl a time series X, I think that X
follows a t-Student pdf but I don’t know the degrees of freedom. How may I
calculate the dof using MLE?
Thank you,
Oscar
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John C Frain
Economics Department
Trinity College Dublin
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Ireland
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