Question

Consider a moving average, MA(1), process $X_t = (e_t + e_{t-1})/2$, where $e_t$ is white noise with unit variance. a) Is this process stationary? Justify your answer. b) Compute the autocorrelation function of the process.

          Consider a moving average, MA(1), process $X_t = (e_t + e_{t-1})/2$, where $e_t$ is white noise with unit variance.
a) Is this process stationary? Justify your answer.
b) Compute the autocorrelation function of the process.

Added by Juan C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

09/14/2023

Step 1

The mean of the process x_t can be calculated as E[x_t] = E[(\epsilon_t + \epsilon_{t-1})/2] = (E[\epsilon_t] + E[\epsilon_{t-1}])/2 = 0, since the white noise has a mean of zero. The variance of the process x_t can be calculated as Var[x_t] = Var[(\epsilon_t + Show more…

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Consider a moving average, MA(1), process x_(t)=(epsi lon_(t)+epsi lon_(t-1))/(2), where epsi lon_(t) is white noise with unit variance. a) Is this process stationary? Justify your answer. b) Compute the autocorrelation function of the process. noise with unit variance. a) Is this process stationary? Justify your answer. b) Compute the autocorrelation function of the process