I tried to create ARCH-GARCH as conditional variance equation but the result of conditional mean analysis (I use ARIMA) shows MA(q) or ARMA(0,0,q) fits conditional mean modelling. Data has ARCH effects.
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Yes, it is possible to have a model where the conditional mean equation is MA(q) while the conditional variance equation is some type of (G)ARCH. Statistically speaking, the conditional mean equation tells us nothing about what the conditional variance equation should be, nor the other way around.
Check out "What is the difference between GARCH and ARMA?" for a broader overview.
Richard Hardy
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