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st: RE: RE: Problems when estimating GARCH(1,1) in STATA
From
Pawel Smietanka <[email protected]>
To
"[email protected]" <[email protected]>
Subject
st: RE: RE: Problems when estimating GARCH(1,1) in STATA
Date
Sat, 3 Aug 2013 12:01:58 +0100
Dear Gustavo,
I followed your advice and set the weight parameter equal to 1. However, this change hasn't bring the results from EViews closer to the results from Stata. I'm very confused and don't really know what I shall do about it. Please find attached again the results from both estimations:
STATA:
arch GDP_REAL_GR L.GDP_REAL_GR L2.GDP_REAL_GR in 32/200, arch(1) garch(1)
(setting optimization to BHHH)
Iteration 0: log likelihood = -251.34499
Iteration 1: log likelihood = -249.86249
Iteration 2: log likelihood = -248.02976
Iteration 3: log likelihood = -244.96325
Iteration 4: log likelihood = -243.4611
(switching optimization to BFGS)
Iteration 5: log likelihood = -243.16209
Iteration 6: log likelihood = -242.87731
Iteration 7: log likelihood = -242.759
Iteration 8: log likelihood = -242.74417
Iteration 9: log likelihood = -242.72715
Iteration 10: log likelihood = -242.72279
Iteration 11: log likelihood = -242.721
Iteration 12: log likelihood = -242.72072
Iteration 13: log likelihood = -242.72072
ARCH family regression
Sample: 1955q4 - 1997q2 Number of obs = 167
Distribution: Gaussian Wald chi2(2) = 7.45
Log likelihood = -242.7207 Prob > chi2 = 0.0241
------------------------------------------------------------------------------
| OPG
GDP_REAL_GR | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
GDP_REAL_GR |
GDP_REAL_GR |
L1. | .096067 .0706532 1.36 0.174 -.0424108 .2345448
L2. | .2064248 .0846426 2.44 0.015 .0405284 .3723211
|
_cons | .5485594 .0975064 5.63 0.000 .3574503 .7396685
-------------+----------------------------------------------------------------
ARCH |
arch |
L1. | .0695061 .0191442 3.63 0.000 .0319843 .107028
|
garch |
L1. | .9419906 .0168409 55.93 0.000 .9089829 .9749982
|
_cons | -.0169108 .0067299 -2.51 0.012 -.0301011 -.0037206
------------------------------------------------------------------------------
EViews:
Dependent Variable: GRR
Method: ML - ARCH (BHHH) - Normal distribution
Date: 08/03/13 Time: 11:54
Sample (adjusted): 1955Q4 1997Q2
Included observations: 167 after adjustments
Convergence achieved after 36 iterations
Bollerslev-Wooldridge robust standard errors & covariance
Presample variance: unconditional
GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 0.734449 0.148615 4.941976 0.0000
GRR(-1) -0.021917 0.114531 -0.191362 0.8482
GRR(-2) 0.055153 0.100287 0.549948 0.5824
Variance Equation
C 0.249905 0.167462 1.492313 0.1356
RESID(-1)^2 0.313131 0.162688 1.924727 0.0543
GARCH(-1) 0.528612 0.199054 2.655618 0.0079
R-squared 0.005515 Mean dependent var 0.675261
Adjusted R-squared -0.006613 S.D. dependent var 1.102948
S.E. of regression 1.106588 Akaike info criterion 3.018091
Sum squared resid 200.8242 Schwarz criterion 3.130115
Log likelihood -246.0106 Hannan-Quinn criter. 3.063559
Durbin-Watson stat 2.051979
I would be grateful about any hints.
Kind regards,
Pawel Smietanka
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of [email protected]
Sent: 02 August 2013 19:47
To: [email protected]
Subject: st: RE: Problems when estimating GARCH(1,1) in STATA
Pawel Smietanka <[email protected]> asked about the differences observed between the coefficient estimates obtained for the same GARCH model specification fitted with the default options for Stata and EViews. Those differences arise because of the treatment for the assumed initial value associated to the conditional variance. By default the -arch- command computes the presample (priming) value "as the expected unconditional variance given the current estimates of the coefficients and any ARMA parameters". The EViews output shown by Pawel reports that the presample variance was obtained by using backcasting with the weight parameter equal to .7. Pawel can obtain the same (or very close) coefficient estimates produced in Stata by setting the weight parameter (in EViews) equal to 1, so that the priming value for the computations would also correspond to the unconditional variance.
I hope that this helps.
--Gustavo
[email protected]
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