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Suppose that you postulate an ARCH(3) model for the volatility of a variable that follows an AR(2) process. Express the whole model mathematically, and explain

Suppose that you postulate an ARCH(3) model for the volatility of a variable that follows an AR(2) process. Express the whole model mathematically, and explain (showing all the steps/details/hypotheses involved) how you would test for the presence of the ARCH effects.

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