5:14 p.m.
Dear all:
I am a new user of gretl.
I have a question about the MLE example for estimating GARCH on page 118 of
the gretl user guide (chapter 17).
I tried the script as shown in what follows ( scalar beta was changed to 0.5
):
========the MLE script===================================
open djclose
series y = 100*ldiff(djclose)
scalar mu = 0.0
scalar omega = 1
scalar alpha = 0.4
scalar beta = 0.5
mle ll = -0.5*(log(h) + (e^2)/h)
series e = y - mu
series h = var(y)
series h = omega + alpha*(e(-1))^2 + beta*h(-1)
params mu omega alpha beta
end mle
===========================================
and the results are:
=========MLE GARCH results==================================
Using numerical derivatives
Tolerance = 1.81899e-012
Function evaluations: 60
Evaluations of gradient: 14
Model 1: ML estimates using the 2526 observations 80/01/04-89/12/29
ll = -0.5*(log(h) + (e^2)/h)
Standard errors based on Outer Products matrix
PARAMETER ESTIMATE STDERROR T STAT P-VALUE
mu 0.0601181 0.0200846 2.993 0.00276 ***
omega 0.724952 936411 0.000 1.00000
alpha 0.238901 0.00594764 40.167 <0.00001 ***
beta 0.132664 701184 0.000 1.00000
Log-likelihood = - 1370.26
Akaike information criterion (AIC) = 2748.53
Schwarz Bayesian criterion (BIC) = 2771.86
Hannan-Quinn criterion (HQC) = 2757
===========================================
and I found the results are different from what estimated by using the
default GARCH estimation , i.e., \Model\Time series\GARCH, in which I got
(as attached below)
I've tried several combinations of initial values for mu, omega, alpha
and, beta. But the results are basically similar.
How can I get closer results from MLE as those from the default GARCH
estimation?
Many thanks
Yi-Nung Yang
====the results from the default GARCH
=======================================
Function evaluations: 75
Evaluations of gradient: 17
Model 2: GARCH estimates using the 2527 observations 80/01/03-89/12/29
Dependent variable: y
Standard errors based on Hessian
VARIABLE COEFFICIENT STDERROR T STAT P-VALUE
const 0.0700980 0.0184927 3.791 0.00015 ***
alpha(0) 0.0483241 0.0114087 4.236 0.00002 ***
alpha(1) 0.0917793 0.0109744 8.363 <0.00001 ***
beta(1) 0.869729 0.0179295 48.508 <0.00001 ***
Mean of dependent variable = 0.047711
Standard deviation of dep. var. = 1.15563
Unconditional error variance = 1.25546
Log-likelihood = -3568.13
Akaike information criterion (AIC) = 7146.26
Schwarz Bayesian criterion (BIC) = 7175.44
Hannan-Quinn criterion (HQC) = 7156.85
===========================================
6:50 p.m.
On Fri, 5 Oct 2007, yinung CYCU wrote:
Dear all:
I am a new user of gretl.
I have a question about the MLE example for estimating GARCH on page 118 of
the gretl user guide (chapter 17).
I tried the script as shown in what follows ( scalar beta was changed to 0.5
):
Hmm. Weird. I copied/pasted your script and I get
Function evaluations: 111
Evaluations of gradient: 26
Model 1: ML estimates using the 2527 observations 80/01/03-89/12/29
ll = -0.5*(log(h) + (e^2)/h)
Standard errors based on Outer Products matrix
PARAMETER ESTIMATE STDERROR T STAT P-VALUE
mu 0.0701074 0.0182281 3.846 0.00012 ***
omega 0.0483072 0.00513289 9.411 <0.00001 ***
alpha 0.0917997 0.00269541 34.058 <0.00001 ***
beta 0.869745 0.00811328 107.200 <0.00001 ***
Log-likelihood = -1245.98
Akaike information criterion (AIC) = 2499.95
Schwarz Bayesian criterion (BIC) = 2523.29
Hannan-Quinn criterion (HQC) = 2508.42
which looks ok. What version of gretl are you using? In you output I see
Function evaluations: 60
Evaluations of gradient: 14
It looks like in your case the iterations stop much earlier than
necessary, thereby producing an "estimate" far away from the true maximum.
Could you please try to see what happens by appending the --verbose switch
to mle?
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
2:31 a.m.
2007/10/5, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it>:
>>On Fri, 5 Oct 2007, yinung CYCU wrote:
>>Could you please try to see what happens by appending the --verbose
switch
>>to mle?
Yes. Please see below and thanks.
Yi-Nung Yang
Chung Yuan Christian University, Taiwan
========================================
gretl version 1.6.5
Current session: 2007/10/05 10:28
? open djclose
Read datafile c:\progra~1\userdata\gretl-1.6.5\data\misc\djclose.gdt
periodicity: 5, maxobs: 2528,
observations range: 1980/01/02-1989/12/29
Listing 2 variables:
0) const 1) djclose
? series y = 100*ldiff(djclose)
Generated series y (ID 2)
? scalar mu = 0.0
Generated scalar mu (ID 3) = 0
? scalar omega = 1
Generated scalar omega (ID 4) = 1
? scalar alpha = 0.4
Generated scalar alpha (ID 5) = 0.4
? scalar beta = 0.5
Generated scalar beta (ID 6) = 0.5
? mle ll = -0.5*(log(h) + (e^2)/h)
? series e = y - mu
? series h = var(y)
? series h = omega + alpha*(e(-1))^2 + beta*h(-1)
? params mu omega alpha beta
? end mle --verbose
Using numerical derivatives
Iteration 1: Log-likelihood = -1561.46147443
Parameters: 0.00000 1.0000 0.40000 0.50000
Gradients: 89.979 -296.97 -181.84 -396.60
Iteration 2: Log-likelihood = -1472.96367506 (steplength = 0.00032)
Parameters: 0.028793 0.90497 0.34181 0.37309
Gradients: 53.018 -274.09 -163.79 -366.04
Iteration 3: Log-likelihood = -1447.77404259 (steplength = 0.00032)
Parameters: -0.064045 0.85520 0.32585 0.30662
Gradients: 231.08 -235.92 -149.60 -315.06
Iteration 4: Log-likelihood = -1444.66210893 (steplength = 0.008)
Parameters: -0.048367 0.80389 0.50576 0.23805
Gradients: 219.45 -197.62 -190.94 -263.91
Iteration 5: Log-likelihood = -1400.66087235 (steplength = 0.04)
Parameters: -0.020901 0.76422 0.39267 0.18469
Gradients: 177.60 -130.52 -156.37 -174.31
Iteration 6: Log-likelihood = -1378.72010975 (steplength = 0.2)
Parameters: 0.0018002 0.75301 0.26579 0.16997
Gradients: 133.04 -86.134 -62.471 -115.03
Iteration 7: Log-likelihood = -1375.43661347 (steplength = 1)
Parameters: 0.088888 0.69792 0.23498 0.095992
Gradients: -74.989 112.68 41.097 150.49
Iteration 8: Log-likelihood = -1370.89509923 (steplength = 1)
Parameters: 0.064386 0.73628 0.22325 0.14732
Gradients: -10.259 -30.131 17.878 -40.239
Iteration 9: Log-likelihood = -1370.84179073 (steplength = 1)
Parameters: 0.053937 0.72411 0.26523 0.13111
Gradients: 15.082 -5.7174 -39.239 -7.6353
Iteration 10: Log-likelihood = -1370.28526304 (steplength = 1)
Parameters: 0.056917 0.72388 0.23809 0.13085
Gradients: 7.8871 4.6573 2.7641 6.2198
Iteration 11: Log-likelihood = -1370.26428037 (steplength = 0.00032)
Parameters: 0.059441 0.72537 0.23898 0.13284
Gradients: 1.6561 -0.82962 -0.38197 -1.1079
Iteration 12: Log-likelihood = -1370.26343966 (steplength = 0.00032)
Parameters: 0.060046 0.72515 0.23888 0.13254
Gradients: 0.17639 -0.021055 0.026967 -0.028467
Iteration 13: Log-likelihood = -1370.26343939 (steplength = 0.00032)
Parameters: 0.060046 0.72515 0.23889 0.13253
Gradients: 0.17676 -0.018224 0.011653 -0.024374
Iteration 14: Log-likelihood = -1370.26343279 (steplength = 1)
Parameters: 0.060119 0.72501 0.23890 0.13262
Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415
Iteration 14: Log-likelihood = -1370.26343279 (steplength = 0.2)
Parameters: 0.060119 0.72499 0.23890 0.13263
Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415
--- FINAL VALUES:
Iteration 14: Log-likelihood = -1370.26343279 (steplength = 0.00032)
Parameters: 0.060118 0.72499 0.23890 0.13263
Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415
Tolerance = 1.81899e-012
Function evaluations: 53
Evaluations of gradient: 14
Model 1: ML estimates using the 2526 observations 80/01/04-89/12/29
ll = -0.5*(log(h) + (e^2)/h)
Standard errors based on Outer Products matrix
PARAMETER ESTIMATE STDERROR T STAT P-VALUE
mu 0.0601181 0.0200801 2.994 0.00275 ***
omega 0.724990 233390 0.000 1.00000
alpha 0.238901 0.00564566 42.316 <0.00001 ***
beta 0.132635 174763 0.000 1.00000
Log-likelihood = -1370.26
Akaike information criterion (AIC) = 2748.53
Schwarz Bayesian criterion (BIC) = 2771.86
Hannan-Quinn criterion (HQC) = 2757
7:13 a.m.
On Fri, 5 Oct 2007, yinung CYCU wrote:
2007/10/5, Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it>:
>
>>> On Fri, 5 Oct 2007, yinung CYCU wrote:
>
>>> Could you please try to see what happens by appending the --verbose
> switch
>>> to mle?
Yes. Please see below and thanks.
[...]
Iteration 1: Log-likelihood = -1561.46147443
Parameters: 0.00000 1.0000 0.40000 0.50000
Gradients: 89.979 -296.97 -181.84 -396.60
[...]
--- FINAL VALUES:
Iteration 14: Log-likelihood = -1370.26343279 (steplength = 0.00032)
Parameters: 0.060118 0.72499 0.23890 0.13263
Gradients: -0.0018076 0.00079581 -0.0017053 0.0013415
This is puzzling. I've tried replicating your results with CVS and 1.6.5
on both Windows and Linux. I *can* replicate your problem, but only with
the Windows version of 1.6.5. Could you please confirm that the current
Windows snapshot works properly? You can download it from the following
URL: http://ricardo.ecn.wfu.edu/pub/gretl/gretl_install.exe
Thanks
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
6601
days inactive
6602
days old
3 comments
2 participants
participants (2)
-
Riccardo (Jack) Lucchetti -
yinung CYCU