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In ARMA model, the error term is assumed to be white noise, i.e. independent and identically distributed. In ARCH model, we relaxed the assumption and let the error term to be uncorrelated but dependent. Then, we specify a structure for the error term. Is my understanding correct? Thanks.

cheezit
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  • cheezit, I was going through my old answers and noticed this one was neither accepted nor upvoted. Do you perhaps need further clarification? – Richard Hardy Jul 29 '17 at 19:13

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Your thinking is mostly correct, but not precisely. ARMA specifies a model for the conditional mean of a time series while GARCH specifies a model for the conditional variance. ARMA and GARCH can be combined, but not necessarily.

  • You can have an ARMA conditional mean model with (1) i.i.d. errors, (2) GARCH errors or (3) other type of errors that are dependent in terms of higher moments.
  • You can have a GARCH conditional variance model for the errors from a conditional mean model that is (1) constant, (2) ARMA, or (3) some other model.

See this thread for more details.

Of course, ARCH is a special case of GARCH and the statements above hold for ARCH just as they do for GARCH.

Richard Hardy
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