How do you prove that GARCH(1,1) = ARCH(infinity)? Need some guidance on how to start on this.


The derivation is already in Bollerslev's original paper (see equation (4) and the discussion around it). In general, this equivalence is identical to the equivalence of an ARMA(p, q) and its AR($\infty$) representation if the stationarity and invertibility conditions are met.

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  • $\begingroup$ can show the proof. just copy and paste the equation here. I am not able to access the whole paper. $\endgroup$ – lakesh Dec 13 '13 at 18:59
  • $\begingroup$ would appreciate your help... $\endgroup$ – lakesh Dec 13 '13 at 18:59
  • $\begingroup$ @lakesh An ungated copy of the paper is available here. $\endgroup$ – tchakravarty Dec 13 '13 at 19:08
  • $\begingroup$ MA(infinite) you mean not AR (infinite) $\endgroup$ – Xavier Dec 3 '16 at 16:19

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