# Why is GARCH(1,1) = ARCH(infinity)?

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.