# Define the order of GARCH(m.s)

• 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 (although i bsed on the result of ACF/PACF of Squared error). 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 GARCH are not available. How can we estimate the order of GARCH(m.s)?

• Why not using the information critera to choose the order? Commented May 25, 2016 at 21:29
• -Continously, 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). Commented May 26, 2016 at 2:50
• -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! Commented May 26, 2016 at 2:51
• I would just calculate AIC and BIC, and choose the best model based on these criteria. Commented May 26, 2016 at 20:57
• Look at the significance of the parameters of your GARCH (2,1) model: it may be that the first GARCH parameter is not significant; in that case, you can set it equal to zero, ending up with a GARCH(1,1). Usually, you do not gain so much by raising up the GARCH order, with respect to the GARCH(1,1); instead, you will be worse in efficiency: this is why I agree with @Egodym on the use of selection criteria. Commented Jun 1, 2016 at 16:51

Checking the ACF/PACF of the squared error term is necessary, although, not sufficient condition. Let's assume the following GARCH (m,s) model $$y_t=a_0+a(L)\varepsilon_t^2+b(L)y_t$$ $$\varepsilon_t=v_t\sqrt{a_0+a(L)\varepsilon_t^2+b(L)y_t }$$ where $v_t$ is a white-noise procedure. There're many other things to investigate:
• Checking the ACF/PACF of the error term. Residuals cannot be autocorrelated. The ARMA model ($y_t=a_0+a(L)\varepsilon_t^2+b(L)y_t$) part of the GARCH model is not correctly specified if the residuals are autocorrelated.
• Checking the ACF/PACF of the squared error term. You can test whether your procedure is a GARCH procedure or not. Equivalently, one can examine Ljung–Box Q-statistics. It can be used to test for groups of significant coefficients. Rejecting the null hypothesis that the $\varepsilon_t^2$ sequence is serially uncorrelated is equivalent to rejecting the null hypothesis of no ARCH or GARCH errors.