[Gretl-devel] RFC: $sigma & co.

[Riccardo (Jack) Lucchetti]

On Wed, 30 Apr 2008, Riccardo (Jack) Lucchetti wrote:

> On Wed, 30 Apr 2008, Allin Cottrell wrote:
>
>> On Mon, 28 Apr 2008, Sven Schreiber wrote:
>> 
>> [re, reorganizing the $sigma and $vcv accessors]
>> 
>>> Although I will be one of the (few?) affected users I agree with
>>> Jack that $vcv should be changed, especially because it's very
>>> simple to change $vcv to $sigma to get the scripts working
>>> again. (And I like the functionality that $vcv will deliver in
>>> VAR/VECM contexts.)
>> 
>> OK.
>
> Coding $vcv for VARs should be quite easy. I'll try to see to that tomorrow. 
> Things are a bit trickier for VECMs. Should we return the v-cov matrix of the 
> coefficients in VECM or VAR form?

I just committed to CVS a few modifications to the VAR code, so that $vcv 
returns the estimated covariance matrix for the coefficients. I don't 
think I've broken anything, but you never know, so please test! 
Limitations:

1) the --robust switch is ignored
2) VECMs aren't handled

Moreover, we have a slight inconsistency in the way we compute things: 
$sigma uses the asymptotic formula (ie, E'E over T), while in the 
displayed equations we use degrees-of-freedom corrected figures for 
standard errors. I'm not overly bothered by this, but some may. Example 
script:

<script>
open denmark
list Y = LRM LRY
scalar order = 2
scalar n = nelem(Y)*order+1
var order Y

b = vec($coeff)
vcv = $vcv
scalar correction = ($nobs-order)/($nobs-order-n)

#reproduce displayed stderrs
se = sqrt(diag(vcv)*correction)

zstat = b./se

eval b~se~zstat
</script>

Comments welcome.

Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti