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### Trouble with R squared GARCH(1,1)

Posted: Thu Aug 08, 2013 3:16 am
Hi all,

Please help me as I got the trouble with R squared when attempting to analysing the daily impact of oil price volatility on the performance of stock market following steps.

Step 1. Collect data of stock and oil price, make the return (ln(Pt+1/Pt)) and add them to Eviews.
Step 2. Group these 2 time series to one spreadsheet and run the quick Estimate equation for ARCH
Step 3. Equation: r_index c r_bre with Student t distribution

Dependent Variable: R_INDEX
Method: ML - ARCH (Marquardt) - Student's t distribution
Date: 08/08/13 Time: 17:05
Sample: 7/31/2000 7/31/2007
Included observations: 1566
Convergence achieved after 18 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)

Variable Coefficient Std. Error z-Statistic Prob.

C -0.000232 0.000159 -1.456417 0.1453
R_BRE 0.006947 0.007364 0.943421 0.3455

Variance Equation

C 3.97E-06 8.34E-07 4.753775 0.0000
RESID(-1)^2 0.624449 0.067885 9.198588 0.0000
GARCH(-1) 0.531662 0.027272 19.49468 0.0000

T-DIST. DOF 5.977412 0.668936 8.935705 0.0000

R-squared -0.009211 Mean dependent var 0.001409
Adjusted R-squared -0.009857 S.D. dependent var 0.016978
S.E. of regression 0.017062 Akaike info criterion -6.194896
Sum squared resid 0.455283 Schwarz criterion -6.174373
Log likelihood 4856.603 Hannan-Quinn criter. -6.187267
Durbin-Watson stat 1.284358

>>>> However, i got the trouble with R squared NEGATIVE?
Any one could explain what wrong i have done???
Many thx

### Re: Trouble with R squared GARCH(1,1)

Posted: Mon Aug 12, 2013 3:00 am
You have done nothing wrong. GARCH models deal with the variance part. Since R-squared is a valid metric only for mean equation, you do not have to worry about its value no matter what the GARCH estimation yields. There are other diagnostics that can be used for checking the validity of your model. Please refer to a textbook for more details.

### Re: Trouble with R squared GARCH(1,1)

Posted: Mon Aug 12, 2013 3:46 am
trubador wrote:You have done nothing wrong. GARCH models deal with the variance part. Since R-squared is a valid metric only for mean equation, you do not have to worry about its value no matter what the GARCH estimation yields. There are other diagnostics that can be used for checking the validity of your model. Please refer to a textbook for more details.

I ask some person but they confirm that the R squared negative in impossible.
As you said, the R-squared here is only explain for the mean equation, not the variance part.
But, my purpose is to study the impact of oil price volatility to stock price.
R_index = a1 + a2*R_oil + epsilon

As the result stated:
Variable Coefficient Std. Error z-Statistic Prob.

C -0.000232 0.000159 -1.456417 0.1453
R_BRE 0.006947 0.007364 0.943421 0.3455

the p_value is material means not significant statisic, R_squared negative >>> does it imply that the GARCH (1,1) is not appropriate to capture and analyse the impact of these 2 time series?
Should i use other model?

PS: I have attached file data, could you please re-test for me.
Many thanks and best regards,

### Re: Trouble with R squared GARCH(1,1)

Posted: Mon Aug 12, 2013 6:50 am
Listen to Trubador. Since you are not doing least squares a negative R-squared is perfectly possible.