I have data from a humidity sensor and would like to estimate the confidence interval of its mean value. However, since the time stamps are "too close together" the data-points are correlated. Therefore, I have to come up with a clever idea to handle the autocorrelation. The following solutions came to my mind:
- Removing neighbouring data-points until they are no longer autocorrelated. This is valid, however, most probably this does not yield the most accurate result.
- First estimating the autocorrelation function $\rho$ and the variance $\sigma^2$, then using
$Var[\bar{X}_i] = \frac{\sigma^2}{N} + (1 - \frac{1}{N}) \rho \cdot \sigma^2$
which is valid if
$E[X_i]=0$, $Var[X_i]=\sigma^2$, and $Cov[X_i, X_j] = \rho \sigma^2$
However there must be more accurate methods using time series analysis, aren't there? This is such a common problem, but I couldn't find an answer.
