st: RE: RE: Problems when estimating GARCH(1,1) in STATA

[Pawel Smietanka <lexps3@nottingham.ac.uk>]

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: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of gsanchez@stata.com
Sent: 02 August 2013 19:47
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: Problems when estimating GARCH(1,1) in STATA

Pawel Smietanka <lexps3@nottingham.ac.uk> 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
gsanchez@stata.com



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