Estimating Constant Mean

Procedure

For a stationary process $Z_t=\mu +X_t$ where $E[X_t]=0$:

1. Calculate the sample mean: $\bar{Z}=\frac{1}{n}{\sum }_{t=1}^n{Z}_t$
2. Assess the precision of $\bar{Z}$ based on the autocovariance of $X_t$. If $X_t$ is white noise: $\mathrm{Var}(\bar{Z})=\frac{{\gamma }_0}{n}$
3. If $X_t$ is autocorrelated, the variance of the sample mean is adjusted by the sum of autocorrelations.