T values are huge, errors very small

[hardmann]

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
@regcrits

set 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
@regcrits


set dj_su = dj_u / sqrt(dj_h)
@bdindtests(number=12) dj_su

set sci_su = sci_u / sqrt(sci_h)
@bdindtests(number=12) sci_su

* US(-1) to china ma(1)-garch

garch(p=1,q=1,regressors,resids=dj_u,hseries=dj_h) / djoc2
# constant  %mvgavge{1} %mvgavge{2}
@regcrits

set dj_u2 = dj_u * dj_u

garch(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
@regcrits


set dj_su = dj_u / sqrt(dj_h)
@bdindtests(number=12) dj_su

set 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

[TomDoan]

Aren't you getting a message like this?:

Code: Select all

NO CONVERGENCE IN 6 ITERATIONS
LAST CRITERION WAS  0.0000000
SUBITERATIONS LIMIT EXCEEDED.
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY HIGHER SUBITERATIONS LIMIT, TIGHTER CVCRIT, DIFFERENT SETTING FOR EXACTLINE OR ALPHA ON NLPAR
RESTARTING 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.

[hardmann]

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.

[TomDoan]

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.