GARCH results interpretation

[James071375]

Hi, folks

I ran the following GARCH model programs.

PROC AUTOREG DATA = COMBINED;
MODEL STD = / GARCH = (P=1, Q= 1) ;
HETERO SNMT / COEF = NONNEG;
RUN;

COMBINED6 is my dataset. STD the monthly standard deviation calculated by daily returns within a month.
SNMT is the independent variable. I'd like to know the relation between STD and SNMT.

GARCH Estimates
SSE 534.553909 Observations 1110
MSE 0.48158 Uncond Var .
Log Likelihood -707.84869 Total R-Square .
SBC 1450.75795 AIC 1425.69737
MAE 0.39453106 AICC 1425.75172
MAPE 36.4932082 HQC 1435.17376
Normality Test 9154.3657
Pr > ChiSq <.0001

Parameter Estimates
Variable DF Estimate Standard
Error t Value Approx
Pr > |t|
Intercept 1 0.6879 0.009208 74.71 <.0001
ARCH0 1 0.0660 0.006499 10.15 <.0001
ARCH1 1 1.2297 0.0611 20.14 <.0001
GARCH1 1 0.0338 0.0260 1.30 0.1929
HET1 1 0.0000771 0.0000452 1.71 0.0879

Could anyone know how to interpret the results? It appears that it didn't show the relation I expect between SNMT and STD. By the way, when I used the OLS regression model, SNMT is significantly negatively related to STD and that's expected results I want. If you any thought, suggestion, or comment, please feel free to let me know. Thank you for your help in advance.

[dw_sas]

Hi @James071375 

The model you are specifying in PROC AUTOREG fits a simple mean model (ie. intercept only) to your dependent variable STD.  It also models the conditional error variance as a GARCH(1,1) model along with your SNMT variable as an input in the model for the variance.  The COEF=NONNEG option in the HETERO statement you are specifying restricts the coefficient associated with SNMT to be non-negative.

Because you are getting unexpected results, you might want to verify this is the model you intend to fit.  The following sections of the PROC AUTOREG documentation should help clarify the model that your current specification is fitting:

https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_expand_details13.htm&docsetVersi... 

https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_autoreg_details12.htm&docsetVers... 

https://go.documentation.sas.com/?docsetId=etsug&docsetTarget=etsug_autoreg_syntax11.htm&docsetVersi... 

If you need additional information, please provide the full mathematical model you are trying to fit (both the equation for the mean and the equation for the variance).  In the meantime, I hope this helps!

DW