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# Time Series - ACVF

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a. Find the ACVF of the time series X_t = Z_t + .3Z_t-1 - .4Z_t-2, where {Z_t} ~ WN(0, 1).

b. Find the ACVF of the time series Y_t = Z_t - 1.2Z_t-1 - 1.6Z_t-2, where {Z_t} ~ WN(0, 25). Compare with the answer found in (a).

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#### Solution Preview

Please see the attachment.

Solution to 2.2. We know that and A and B are two uncorrelated random variables with mean 0 and variance 1, that is, .
So,
So, by the linearity of expected value, we have

(1)
(2) Since , by the linearity of expected ...

#### Solution Summary

In terms of the time series, extensive calculations are completed step by step to calculate the ACVF.

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