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Suppose that $e(t)$ is a white noise process, and consider the process $Y(t) = μ + e(t) - e(t-1).$

Show that the process is stationary and compute its autocovariance function and ACF?

Please help, I've been trying to find information about this question for hours and I can't find any straight forward information.

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Hints:$\mathbb{E}[Y(t)]=\mathbb{E}[\mu+e(t)-e(t-1)]=\mu$ $\mathbb{E}[Y(t)Y(s)]=\mu^2+\mathbb{E}[(e(t)-e(t-1))(e(s)-e(s-1))]$ $e(t)$ is white noise process, so $E[e(a)e(b)]=D[e(a)]=\sigma^2$ if $a=b$ and 0 otherwhise. When process is stationary? Can you finish it now?

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    Do you mean $e(a)$ and $e(b)$ by "they"? Independence of something doesn't imply stationarity, you have to check whether mean $E[Y(t)]$ is constant (done) and how behaves autocovariance function2012-04-05