GARCH Effects

[Michelle]

Dear Forum participants,

Firstly I would like to introduce myself: my name is Michelle and I am a new member in this forum. I am currently estimating a model for sovereign yield spreads, to which I have introduced a group of various GARCH effects, to capture clusters of volatility that characterize periods of financial crises.
Sum of the coefficients in the variance equation (α+β in the GARCH(1,1) case, for example) which is close to one, normally indicates that volatility shocks are persistent. For some reason, I get sums that exceed 1. All tests indicate the right specification of the model (the residuals are stationary, normally distributed, and there is no ARCH up to order 6 in the residuals according to an ARCH LM test).

Does anybody in the forum have an idea why this could happen? In my opinion it might make sense to happen for a very limited period, however could not persist for the long term. My data includes 110 monthly averages, which is not a small sample.

Looking forward to hearing from you, and thanking you kindly in advance,

Michelle.

[trubador]

Could you please also post your workfile?

[Michelle]

Dear Trubador,

Many thanks for your prompt reply. Unfortunately, I am not allowed to post the raw data, due to copy rights issues (these are J.P. Morgan's Russia's soverign yield spreads, in basis points). I am therefore sending one of the EViews cointegration outputs, that reflects the too-big coefficient of the ARCH effect (3.335), I hope you could see it properly:


Dependent Variable: RUSSIA
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 05/16/09 Time: 22:30
Sample (adjusted): 2 114
Included observations: 113 after adjustments
Convergence achieved after 1 iteration (for starting values)
Convergence achieved after 189 iterations
Bollerslev-Wooldrige robust standard errors & covariance
Variance backcast: ON
RUSSIA=C(1)+C(2)*RUSSIA(-1)+C(5)*EMBI+C(6)*EMBI(-1)
+RESIMP^C(11)+C(12)*PUTIN+C(14)*BREAK0901
GARCH = C(15) + C(16)*RESID(-1)^2 + C(17)*GARCH(-1)


Coefficient Std. Error z-Statistic Prob.


C(1) 282.9674 31.93084 8.861884 0.0000
C(2) 0.706208 0.012830 55.04292 0.0000
C(5) 0.591455 0.012364 47.83846 0.0000
C(6) -0.442136 0.016106 -27.45199 0.0000
C(11) -10.39373 0.018478 -562.4941 0.0000
C(12) -115.9567 25.19568 -4.602245 0.0000
C(14) -161.9733 8.158301 -19.85380 0.0000


Variance Equation


C 16.79125 6.614167 2.538679 0.0111
RESID(-1)^2 3.334717 0.576151 5.787926 0.0000
GARCH(-1) -0.005646 0.007380 -0.765121 0.4442


R-squared 0.994787 Mean dependent var 624.3633
Adjusted R-squared 0.994332 S.D. dependent var 805.6266
S.E. of regression 60.65321 Akaike info criterion 9.535992
Sum squared resid 378917.6 Schwarz criterion 9.777354
Log likelihood -528.7836 Durbin-Watson stat 2.305530




Have you ever received such a thing?

Have a great day and looking forward to hearing from you,

Michelle.

[trubador]

OK then. Try adding several AR(p) coefficients into your mean equation and see if they are significant. Spread values are usually not stationary, so you may wish to use changes instead of levels. You should really make sure that the mean equation is stationary before deciding the GARCH specification.

[Michelle]

Dear Trubador,

This is actually a cointegration model. Russia's spreads are indeed I(1), rather than I(0), however also one of the explanatory variables (spreads of other countries), and therefore, if there is cointegration, the residuals should be stationary, and they really are.
I have also tried to introduce more lags of the variables, however excluded them since they were not found significant (Hendry's approach).

Do you think that the odd coefficient I received for the ARCH term indicates misspecification of the mean equation?

Many thanks again for your kind help,

Michelle.

[trubador]

It is really hard to say without looking into your variables' properties along with the model.It seems your mean equation is also nonlinear, and the estimated GARCH coefficient is insignificant. There may be plenty of reasons why you obtain such results. For the moment, I cannot think of any other problem than the misspecification of the model. Other users in the forum might have a better idea and may come up with a more satisfactory solution.

[Michelle]

Many thanks, Trubador, I truly appreciate it.

Michelle.