SHAZAM Questions and Answers (Q&A) - RSS feedhttp://community.econometrics.com/questions/SHAZAM Econometrics, Statistics and Analytics Communityen<font color="white">Copyright <b>SHAZAM Analytics, 2018</b></font>Sun, 03 Nov 2013 02:31:09 +0000ARCH with Exogenous Variableshttp://community.econometrics.com/question/392/arch-with-exogenous-variables/Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.Mon, 21 Oct 2013 12:52:20 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/Comment by SHAZAMHelp for <p>Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=394#post-id-394Can you publish the sample data, commands and output for each please. Note that SHAZAM has numerous options on the HET command including 3 optimization methods. Suggest you also confirm the nature of the heteroskedasticity specified. e.g. multiplicative, dependent variable heteroskedascity etcMon, 21 Oct 2013 18:16:08 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=394#post-id-394Comment by stat78 for <p>Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=398#post-id-398I am running a model where the index variable is in the ARCH equation for the variance. How would you call that type of het specification? Thank you for your help!
In SHAZAM I am running
het price index interaction lag1_pri (index) / arch=1
In SAS I am running
PROC AUTOREG DATA=test;
m1: model price=lag1_pri index interaction/ garch=(p=1) MAXITER = 1000 NOMISS;
hetero index ;
run;
OUTPUT SHAZAM:
FINAL STATISTICS :
TIME = 0.0290 SEC. ITER. NO. 28 FUNCTION EVALUATIONS 48
LOG-LIKELIHOOD FUNCTION= -161.1532
COEFFICIENTS
0.8023219 -0.4499052E-01 0.7363933 1.043197 0.4605022
1.850979 -0.3225361 -0.3241526
GRADIENT
0.1081076E-01 0.1721445 0.1343623 -0.1907942E-02 -0.3892096E-01
-0.1332209E-02 -0.4898605E-01 -0.2773277E-02
...WARNING..STATIONARITY CONSTRAINTS NOT SATISFIED
SQUARED CORR. COEF. BETWEEN OBSERVED AND PREDICTED 0.77349
ASY. COVARIANCE MATRIX OF PARAMETER ESTIMATES IS ESTIMATED USING
THE INFORMATION MATRIX
LOG OF THE LIKELIHOOD FUNCTION = -161.153
ASYMPTOTIC
VARIABLE ESTIMATED STANDARD T-RATIO PARTIAL STANDARDIZED ELASTICITY
NAME COEFFICIENT ERROR -------- P-VALUE CORR. COEFFICIENT AT MEANS
MEAN EQUATION:
INDEX 0.80232 0.2749 2.919 0.004 0.273 0.1455 0.0673
INTERACTION -0.44991E-01 0.5196E-01 -0.8659 0.387-0.084 -0.0650 -0.0264
LAG1_PRI 0.73639 0.4716E-01 15.62 0.000 0.835 0.7398 0.7349
CONSTANT 1.0432 0.2235 4.667 0.000 0.413 0.0000 0.1749
VARIANCE EQUATION:
ALPHA_ 0.46050 0.1575 2.924 0.003 0.27
ALPHA_ 1.8510 0.4090 4.525 0.000 0.40
INDEX -0.32254 0.1621 -1.990 0.047-0.19
DELTA_ -0.32415 0.7822 -0.4144 0.679-0.04
OUTPUT SAS:
The SAS System
The AUTOREG Procedure
Model m1
Dependent Variable price
Ordinary Least Squares Estimates
SSE 189.458072 DFE 110
MSE 1.72235 Root MSE 1.31238
SBC 400.371279 AIC 389.426486
MAE 0.81817859 AICC 389.793458
MAPE 14.0623221 HQC 393.868364
Durbin-Watson 1.6752 Regress R-Square 0.7813
Total R-Square 0.7813
Parameter Estimates
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 0.6646 0.3902 1.70 0.0914
lag1_pri 1 0.8831 0.0713 12.39 <.0001
index 1 0.2285 0.6234 0.37 0.7147
interaction 1 -0.0201 0.0963 -0.21 0.8348
Algorithm converged.
GARCH Estimates
SSE 220.488979 Observations 114
MSE 1.93411 Uncond Var .
Log Likelihood -163.52564 Total R-Square 0.7455
SBC 360.204675 AIC 341.051286
MAE 0.8403631 AICC 342.10789
MAPE 14.4105538 HQC 348.824573
Normality Test 98.6849
Pr > ChiSq <.0001
Parameter Estimates
Standard Approx
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 1.2851 0.2705 4.75 <.0001
lag1_pri 1 0.6961 0.0770 9.05 <.0001
index 1 0.3839 0.4185 0.92 0.3590
interaction 1 0.0150 0.0918 0.16 0.8704
ARCH0 1 0.2979 0.0686 4.34 <.0001
ARCH1 1 1.5883 0.2667 5.96 <.0001
HET1 1 0 0 . .Tue, 29 Oct 2013 11:20:09 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=398#post-id-398Comment by stat78 for <p>Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=399#post-id-399I should probably make it a very specific question. I want to run an ARCH(1) model where a have an independent indicator variable in the variance ARCH equation as a linea term i.e. h= const+ARCH(1)+b*indicator.
So far I have been using het price index interaction lag1_pri (index) /arch=1
Is this the right syntax? I cannot assign model=varlin for a linear term with ARCH. What is the proper way to do it? Thanks.Tue, 29 Oct 2013 14:17:02 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=399#post-id-399Comment by stat78 for <p>Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=403#post-id-403Thank you for your reply.How about my second question regarding the functional form of the exogenous variable?Fri, 01 Nov 2013 17:15:03 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=403#post-id-403Answer by SHAZAMHelp for <p>Shazam and SAS produce very different results when running an ARCH model with an exogenous variable. I am using Proc autoreg in SAS with a hetero statement. What can explain the difference? Thanks.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?answer=400#post-id-400For an ARCH(1) model, the SHAZAM statement simply needs the option ARCH=1 which has been set correctly. The specification of exogenous variable variance with index by listing (index) after the list of independent variables is also correct.
In the SAS model it appears from their online documentation that an ARCH(1) model would need the option GARCH=(P=0,Q=1) not GARCH=(P=1) which appears to fit a GARCH(1,1) model. The SAS documentation does not clearly indicate how to specify the same form of exogenous variable variance with the hetero statement.
Note that in SHAZAM you can check for the presence of heteroskedasticity using the DIAGNOS / HET statement following an OLS command to perform Lagrange Multipler Tests (including a test for ARCH=1 errors). Page 246 of the SHAZAM 11 manual has further details.
Thu, 31 Oct 2013 17:00:30 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?answer=400#post-id-400Comment by stat78 for <p>For an ARCH(1) model, the SHAZAM statement simply needs the option ARCH=1 which has been set correctly. The specification of exogenous variable variance with index by listing (index) after the list of independent variables is also correct.</p>
<p>In the SAS model it appears from their online documentation that an ARCH(1) model would need the option GARCH=(P=0,Q=1) not GARCH=(P=1) which appears to fit a GARCH(1,1) model. The SAS documentation does not clearly indicate how to specify the same form of exogenous variable variance with the hetero statement.</p>
<p>Note that in SHAZAM you can check for the presence of heteroskedasticity using the DIAGNOS / HET statement following an OLS command to perform Lagrange Multipler Tests (including a test for ARCH=1 errors). Page 246 of the SHAZAM 11 manual has further details.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=401#post-id-401Thank you so much for your reply. A few more follow-up questions.
1) Is there anything in SHAZAM that does not allow me to have the exogenous and the independent variable be the same? I am trying to replicate a study which uses the model that I was referring to.
2) In the variance equation, does the exogenous variable appear in a linear or exponential form. In other words, do we have sigma=ARCH(1) +b*exog or sigma=ARCH(1) +expon(b*exog). I know STATA has multiplicative heteroskedasticity in exponential form and SAS has it linear.
Thanks again!Fri, 01 Nov 2013 09:12:22 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=401#post-id-401Comment by SHAZAMHelp for <p>For an ARCH(1) model, the SHAZAM statement simply needs the option ARCH=1 which has been set correctly. The specification of exogenous variable variance with index by listing (index) after the list of independent variables is also correct.</p>
<p>In the SAS model it appears from their online documentation that an ARCH(1) model would need the option GARCH=(P=0,Q=1) not GARCH=(P=1) which appears to fit a GARCH(1,1) model. The SAS documentation does not clearly indicate how to specify the same form of exogenous variable variance with the hetero statement.</p>
<p>Note that in SHAZAM you can check for the presence of heteroskedasticity using the DIAGNOS / HET statement following an OLS command to perform Lagrange Multipler Tests (including a test for ARCH=1 errors). Page 246 of the SHAZAM 11 manual has further details.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=402#post-id-402Actually, it is possible to specify the same variable in the list of independent variables and in the list of exogenous variables. I have corrected the answer.
Multiplicative heteroskedasticity can be specified using the MODEL=MULT and the exact form of the error variance is specified on page 249 of the SHAZAM 11 manual while in a non-multiplicative form the exact form is specified on page 242.
In the multiplicative form the variance is specified as: h(t) = exp(Z'(t).alpha) as in Harvey [1976, 1990].Fri, 01 Nov 2013 16:52:07 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=402#post-id-402Comment by stat78 for <p>For an ARCH(1) model, the SHAZAM statement simply needs the option ARCH=1 which has been set correctly. The specification of exogenous variable variance with index by listing (index) after the list of independent variables is also correct.</p>
<p>In the SAS model it appears from their online documentation that an ARCH(1) model would need the option GARCH=(P=0,Q=1) not GARCH=(P=1) which appears to fit a GARCH(1,1) model. The SAS documentation does not clearly indicate how to specify the same form of exogenous variable variance with the hetero statement.</p>
<p>Note that in SHAZAM you can check for the presence of heteroskedasticity using the DIAGNOS / HET statement following an OLS command to perform Lagrange Multipler Tests (including a test for ARCH=1 errors). Page 246 of the SHAZAM 11 manual has further details.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=404#post-id-404The reason I am asking is once you specify model=arch you can no longer use model=linear or model=multi. Thus, even though you can have an exogenous variable with arch it is not clear what the functional form is.Fri, 01 Nov 2013 23:24:38 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=404#post-id-404Comment by SHAZAMHelp for <p>For an ARCH(1) model, the SHAZAM statement simply needs the option ARCH=1 which has been set correctly. The specification of exogenous variable variance with index by listing (index) after the list of independent variables is also correct.</p>
<p>In the SAS model it appears from their online documentation that an ARCH(1) model would need the option GARCH=(P=0,Q=1) not GARCH=(P=1) which appears to fit a GARCH(1,1) model. The SAS documentation does not clearly indicate how to specify the same form of exogenous variable variance with the hetero statement.</p>
<p>Note that in SHAZAM you can check for the presence of heteroskedasticity using the DIAGNOS / HET statement following an OLS command to perform Lagrange Multipler Tests (including a test for ARCH=1 errors). Page 246 of the SHAZAM 11 manual has further details.</p>
http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=405#post-id-405It is linear in that case (see pg 242). Yes, the MODEL= option switches between each form of heteroskedasticity.Sun, 03 Nov 2013 02:31:09 +0000http://community.econometrics.com/question/392/arch-with-exogenous-variables/?comment=405#post-id-405