## T values are huge, errors very small

Discussions of ARCH, GARCH, and related models

### T values are huge, errors very small

Dear Tom:

following with hamao et al.(1990), I estimate the spillover effect between USA and China,eg, Dowjones(DJ) and Shanghai composite index (SCI).
I used the two-stages method with MA(1)-GARCH(1,1)-M. Firstly, I estimate individul market with index of open to close. Secondly, I take the square residual derived from first stage as exogenous varible and append it to second market's conditional variance, append the return of first market to second market 's equation.
In seond estimation,all prarameter's T values are huge, errors very small, p value zero.
I guess such estimation anormal.

Code: Select all
`open data "e:\my docs\working\china_us\dj_sci.xls"data(format=xls,org=columns) 1 1157 dj_open dj_close sci_open sci_close*set scico = 100.0*log(sci_open/sci_close{1})set scioc = 100.0*log(sci_close/sci_open)set scicc = 100.0*log(sci_close/sci_close{1})set djco = 100.0*log(dj_open/dj_close{1})set djoc = 100.0*log(dj_close/dj_open)set djcc = 100.0*log(dj_close/dj_close{1})set djoc2 = 1.0 * djoc{1}* stocks spillover from china to US MA(1)-garch-M* firstly, individul china market ma(1)-garch-M garch(p=1,q=1,regressors,resids=sci_u,hseries=sci_h) / scioc# constant  %mvgavge{1}  %garchv@regcritsset sci_u2 = sci_u * sci_u* secondly, introduce  scioc and sci_u2 as exogenous varible both in mean and variance equation of US stocks market.garch(p=1,q=1,regressors,xreg,method=bfgs,iters=100,\$pmethod=simplex, piters=10,resids=dj_u,hseries=dj_h)  / djco# constant %mvgavge scioc %garchv# sci_u2@regcritsset dj_su = dj_u / sqrt(dj_h)@bdindtests(number=12) dj_suset sci_su = sci_u / sqrt(sci_h)@bdindtests(number=12) sci_su* US(-1) to china ma(1)-garchgarch(p=1,q=1,regressors,resids=dj_u,hseries=dj_h) / djoc2# constant  %mvgavge{1} %mvgavge{2}@regcritsset dj_u2 = dj_u * dj_ugarch(p=1,q=1,regressors,xreg,method=bfgs,iters=100,\$pmethod=simplex, piters=5,resids=sci_u,hseries=sci_h) / scico# constant %mvgavge djoc2 %garchv# dj_u2@regcritsset dj_su = dj_u / sqrt(dj_h)@bdindtests(number=12) dj_suset sci_su = sci_u / sqrt(sci_h)@bdindtests(number=12) sci_su`

GARCH Model - Estimation by BFGS
Convergence in 4 Iterations. Final criterion was 0.0000000 <= 0.0000100
Dependent Variable DJCO
Usable Observations 1156
Log Likelihood 287.6747

Variable Coeff Std Error T-Stat Signif
*************************************************************************************
1. Constant 0.0264 5.6931e-007 46380.43427 0.00000000
2. Mvg Avge 0.8277 3.3995e-006 243485.65617 0.00000000
3. SCIOC -0.1444 6.7860e-007 -212779.25373 0.00000000
4. GARCH-V -0.1045 2.0053e-006 -52115.00421 0.00000000
5. C 0.0136 7.3188e-007 18591.52282 0.00000000
6. A 0.0466 1.5554e-006 29964.35221 0.00000000
7. B 0.5844 8.4330e-007 693006.06766 0.00000000
8. SCI_U2 2.5194e-003 3.2238e-007 7814.77028 0.00000000

Information Criteria
AIC -0.484
SBC -0.449
Hannan-Quinn -0.471
(log) FPE -0.484
hardmann
Attachments
dj_sci.xls
Last edited by hardmann on Thu Sep 01, 2011 7:53 am, edited 6 times in total.
hardmann

Posts: 48
Joined: Sat Feb 26, 2011 10:49 pm

### Re: T values are huge, errors very small

Aren't you getting a message like this?:

Code: Select all
`NO CONVERGENCE IN 6 ITERATIONSLAST CRITERION WAS  0.0000000SUBITERATIONS LIMIT EXCEEDED.ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULTTRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPARRESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES MIGHT ALSO WORK`

Don't try to interpret the results when you get a message like that. The reason it's in all CAPS is to warn you that the results are likely nonsense.

You're adding same day squared residuals from the Chinese market to the volatility equation for the U.S. That changes rather dramatically the behavior of that equation. Our guess values for GARCH assume that any additional variables have a relatively small effect compared to the "own" lagged squared residuals and variance. That's no longer true in your model. As a result, you may need to do more experimenting with settings for the non-linear optimization than would be required with a standard GARCH. Perhaps using more simplex iterations, then using BHHH rather than BFGS for finishing off.
TomDoan

Posts: 2761
Joined: Wed Nov 01, 2006 5:36 pm

### Re: T values are huge, errors very small

I get such message of NO CONVERGENCE while using default command without option of " pmethod".
When I add option " pmethod=simplex, piters=10 " in command, such message disappear, but coef. with large T value and samll errors appear. However, when I change number of piters, I get different results, sometimes, get agian warning message .
In such circumstance, BHHH get wores result than BFGS.
hardmann

Posts: 48
Joined: Sat Feb 26, 2011 10:49 pm

### Re: T values are huge, errors very small

Which means that it's a very hard model to fit. It sounds as if you may need to do quite a bit of experimenting in order to get the model to fit properly. The source of the difficulty is the lagged squared "other" residual in the variance equation, so you might want to try starting with a simpler mean model. For instance, why are you including a moving average term? Until you've fit the model with the more complicated variance structure, you have no idea whether the residuals are serially correlated.
TomDoan

Posts: 2761
Joined: Wed Nov 01, 2006 5:36 pm