AMS316 HW6 (Due Dec 12, 2011) 1. Consider the AR(1) process, X t = μ + αX t-1 + Z t , where Z t are i.i.d. standard normal random variables. Derive the least square estimates for μ and α by minimizing S ( μ,α ) = n X t =1 ( X t-μ-αX t-1 ) 2 . 2. For the MA(1) model given by X t = Z t + θZ t-1 and observations X 1 ,...,X N , show that the 1-step ahead forecast b X N (1) = θZ N and that the h-step ahead forecast b X N ( h ) = 0 for h = 2 , 3 ,... . 3. For the AR(1) model given by
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Probability theory, probability density function, normal random variables, ahead forecast XN