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Question

For the following MA (3) process  y t  =  μ  +  Ε t  +  θ 1 Ε t -1  +  θ 2 Ε t -2  +  θ 3 Ε t -3  , where  σ t  is a zero mean white noise process with variance  σ 2

A ACF = 0 at lag 3 Correct Answer Incorrect Answer
B ACF =0 at lag 5 Correct Answer Incorrect Answer
C ACF =1 at lag 1 Correct Answer Incorrect Answer
D ACF =0 at lag 2 Correct Answer Incorrect Answer
E ACF = 0 at lag 3 and at lag 5 Correct Answer Incorrect Answer

Solution

MA(q) process only has memory of length q. This means that all of the autocorrelation coefficients will have a value of zero beyond lag q. This can be seen by examining the MA equation, and seeing that only the past q disturbance terms enter into the equation, so that if we iterate this equation forward through time by more than q periods, the current value of the disturbance term will no longer affect y. Finally, since the autocorrelation function at lag zero is the correlation of y at time t with y at time t (i.e. the correlation of y_t with itself), it must be one by definition.

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