7:52 p.m.
Hi,
I was just wondering what estimation method is used exactly in the
Johansen_stage_1 function (the first step, VAR estimation, of the
Johansen test) of lib/var.c. From looking at the code, it seems like
it might be the 2-step Least Squares method -- but I'm not clear on
where in the code the fitted values are plugged in, it's almost as if
X is never changed between the first and second OLS. Also the comment
refers to log-likelihood.
So is it 2SLS, or is it some maximum likelihood method like FIML? (or
something else)
Thanks,
Simon
9:03 p.m.
On Wed, 5 Oct 2011, Simon Ouellette wrote:
Hi,
I was just wondering what estimation method is used exactly in the
Johansen_stage_1 function (the first step, VAR estimation, of the
Johansen test) of lib/var.c. From looking at the code, it seems like
it might be the 2-step Least Squares method -- but I'm not clear on
where in the code the fitted values are plugged in, it's almost as if
X is never changed between the first and second OLS. Also the comment
refers to log-likelihood.
So is it 2SLS, or is it some maximum likelihood method like FIML? (or
something else)
It isn't 2SLS; it's just plain OLS --- which in this special case happens
to be a simple way to get FIML (for the VEC model the unrestricted ML
estimator can be computed in closed form, and OLS is a nice and simple way
to do it). And yes, the 2nd time ols is executed the regressors are
exactly the same.
In practice, the C function johansen_stage_1 is nearly a step-by-step C
translation[*] of the algorithm described in section 2.2 of Johansen
(1995) "Likelihood-based inference in cointegrated vector autoregressive
models", Oxford University Press. If you're even remotely interested in
time-series analysis, that book is a classic must-read.
It's nice having people who read the source and ask questions. It feels
good!
[*] Looking at the code, it occurs to me that it may be possible to make
it computationally a bit more efficient, possibly at the expense of
readability, but I don't think that anyboby has ever complained about the
"vecm" command being slow, right?
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
3:32 p.m.
Le 05/10/2011 22:03, Riccardo (Jack) Lucchetti a écrit :
but I don't think that anyboby has ever complained about the
"vecm"
command being slow, right?
indeed it isn't! but plotting the combined impulse
responses with their
confidence error is somewhat slow! Maybe this is more a gnuplot concern
than gretl's and I don't know if it can be fixed!
best,
artur
3:39 p.m.
On Thu, 6 Oct 2011, artur bala wrote:
Le 05/10/2011 22:03, Riccardo (Jack) Lucchetti a écrit :
> but I don't think that anyboby has ever complained about the "vecm"
> command being slow, right?
indeed it isn't! but plotting the combined impulse responses with their
confidence error is somewhat slow! Maybe this is more a gnuplot concern
than gretl's and I don't know if it can be fixed!
That's slow because it depends on a complicated bootstrapping
routine. It could maybe be tweaked a little for speed but
basically it's just an inherently time-consuming operation:
the VECM has to be estimated hundreds of times.
Allin Cottrell
4:49 p.m.
On Thu, 6 Oct 2011, Allin Cottrell wrote:
On Thu, 6 Oct 2011, artur bala wrote:
> Le 05/10/2011 22:03, Riccardo (Jack) Lucchetti a écrit :
>> but I don't think that anyboby has ever complained about the
"vecm"
>> command being slow, right?
> indeed it isn't! but plotting the combined impulse responses with their
> confidence error is somewhat slow! Maybe this is more a gnuplot concern
> than gretl's and I don't know if it can be fixed!
That's slow because it depends on a complicated bootstrapping routine. It
could maybe be tweaked a little for speed but basically it's just an
inherently time-consuming operation:
the VECM has to be estimated hundreds of times.
Hmmm, this case may make it worthwhile. The speedup I had in mind was to
coalesce the two preliminary regressions into one. Those regressions have
the same explanatory variables, which are the lagged differences (plus
maybe some extra stuff). For a large number of lags, the matrix that has
to be inverted may be in the order of 20-30 rows/columns, so doing it
twice may make for a nice speedup. Even if we managed to shave off a 10%
of the total CPU time, that may be noticeable when bootstrapping.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
4:52 p.m.
On Thu, 6 Oct 2011, Riccardo (Jack) Lucchetti wrote:
For a large number of lags, the matrix that has to be inverted
may be in the order of 20-30 rows/columns, so doing it twice may make for a
nice speedup.
Heh. That should have read "doing it once instead of twice". Sorry for the
noise.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
9:03 p.m.
On Wed, 5 Oct 2011, Simon Ouellette wrote:
I was just wondering what estimation method is used exactly in the
Johansen_stage_1 function (the first step, VAR estimation, of the
Johansen test) of lib/var.c. From looking at the code, it seems like
it might be the 2-step Least Squares method -- but I'm not clear on
where in the code the fitted values are plugged in, it's almost as if
X is never changed between the first and second OLS. Also the comment
refers to log-likelihood.
It's two applications of OLS (not two-stage least squares), as
described in Hamilton's "Time Series Analysis", section 20.2.
The first set of equations is a VAR in first differences; the
second set has the same regressors as the first, but the
dependent variable in each equation is a first lag in place of
a first difference. There's no use of fitted values; all we
need from these regressions are the residuals, so we can
compute the variance matrices that form the input to the
eigen-analysis.
OLS is MLE for a VAR.
Allin Cottrell
4831
days inactive
4832
days old
6 comments
4 participants
participants (4)
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Allin Cottrell -
artur bala -
Riccardo (Jack) Lucchetti -
Simon Ouellette