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I'm trying to estimate parameters of GARCH(p,q) model. I tried p=1, q=1 with t-distribution errors. Ljung-Box showed no correlation in residuals and squared residual. But the null hypothesis that ARCH-term's coefficient equals 0 was not rejected. So I tried p=0, q=1. Ljung-Box indicated serial correlation in residuals and squared residuals. Moreover, AIC and SC chose the former model. Should I choose GARCH(1,1), though one coefficient is statistically insignificant ?

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    $\begingroup$ I dont see why the ARMA residual being non-zero is a problem. ARMA-Garch models are fairly common in the literature. Maybe I dont understand your question. $\endgroup$ – Drew Nov 11 '14 at 15:43
  • $\begingroup$ It seems to me that the first model is better than the second one, but null hypothesis of one coefficient being zero is not rejected. But when I remove the variable corresponding to this coefficient from the model, I get worse results. $\endgroup$ – user1786577 Nov 11 '14 at 16:29
  • $\begingroup$ It seems that the former model is closer to the answer. It may just be within the significance bounds, try a tighter confidence interval and compare with other softwares for numerical issues $\endgroup$ – Drew Nov 11 '14 at 16:50
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I would keep the model with p=1 and q=1 even those the null hypothesis that ARCH-term's coefficient equals 0 was not rejected. The reason is that (generally) the less autocorrelations there are in the resulting serie, the more accurate your forecast will be. Indeed if you estimate a model and leaves some autocorrelation it means it is still possible to improve your model by taking benefit of these autocorrelations to produce more accurate forecast. SIC and AIC may be sometime misleading since they only care on specific statistical properties (likelihood, number of parameters...).

Finally to be sure, I would recommend you to produce forecasts and to keep the "best" model based on a bunch of loss functions.

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I have many materials about GARCH model (Applied Time series econometrics,page198 ; Econometrics by example- Damodar Gujarati p.238; Introductory econometrics for finance - Chris Brooks p.379) to figure out the Order of Garch(m,s). ​

-All indicate that if the order of ARCH is over 3, use GARCH. And as the order of ARCH increases to infinity, ARCH(m) is equivalent to GARCH(1,1).

  • Also, GARCH(1,1) is proved to be useful to model the return of financial asset and rarely used in any higher order model.​ - But my result show that the coefficent of mean equation (Logreturn)is not significant with the P of 0.148. It show the rejection of GARCH(1,1). But another GARCH(2,1) and (3,1) is significant. Please give me suggestion ! Thank you!
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I know that if the order of Arch(m) is over 3, we should use GARCH and GARCH(1,1) was proved to be the best. But was GARCH(1,1) proved to be available for any country's stock market?

  • My result show that GARCH(1,1) is not statistically significant. However, the Garch(2,1) (3,1) (4,1) (5,1) (6,1) (7,1) (8,1) are statistically significant.

  • Consequently, i conflict that the method based on the ACF/PACF of the Squared return or Squared error to define the Order of ARCH are not available. How can we estimate the order of GARCH(m.s)?

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