ARCH effect after fitting GARCH(1,1)

[Lexie Wang]

I am trying to messure volatility of return on stock index by using GARCH(1,1) but the ARCH-LM test results show that there is ARCH effect in the residuals after fitting GARCH(1,1). I used ARIMA for the mean equation. I also tried GARCH(1,2) and GARCH(2,1) but there is still ARCH effect. How can I solve this problem in Stata? Great thanks to any help!

[Sven-Kristjan Bormann]

The ARCH-LM test should work only after regress and not after the arch-command. Therfore, I don't understand where you get your results from.
In order to help you, you post an example of your dataset by running the dataex-command and showing the output here + the command that you actually ran.

[Lexie Wang]

The ARCH-LM test should work only after regress and not after the arch-command. Therfore, I don't understand where you get your results from.
In order to help you, you post an example of your dataset by running the dataex-command and showing the output here + the command that you actually ran.

Thank you for your reply.

There are four time periods so I have four models. I determined the arima model for each time period by information criteria then used arima-arch model to try eliminating arch effect. After extracting the residuals from arch-arima model and regressing it on constant, however, I found the residuals still have arch effect even after garch for the first and second time period. The residuals for the third and fourth period do not have arch effect after garch. What should I do now to completely eliminate the arch effect of the arch-arima residuals for the first and second period?

The code is as follows.

**arch with arima
arch return if t<419, arch(1/2) garch(1/1) arima(2,0,2) het(d1) nolog
est store arch1
predict e_1 if t<419,r
reg e_1
estat archlm,lag(1/15)

arch return if t<712 & t>272, arch(1/1) garch(1/1) arima(7,0,5) het(d2) nolog
est store arch2
predict e_2 if t<712 & t>272,r
reg e_2
estat archlm,lag(1/15)

arch return if t<804 & t>418, arch(1/1) garch(1/1) arima(3,0,3) het(d3) nolog
est store arch3
predict e_3 if t<804 & t>418,r
reg e_3
estat archlm,lag(1/15)

arch return if t>711, arch(1/1) garch(1/1) het(d4) nolog
est store arch4
predict e_4 if t>711,r
reg e_4
estat archlm,lag(1/15)