# Time Series - ACVF

Please see the attached file for full problem description.

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).

© BrainMass Inc. brainmass.com October 9, 2019, 3:49 pm ad1c9bdddfhttps://brainmass.com/statistics/time-series-analysis/time-series-acvf-13901

#### 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.

$2.19