Hi @caesoma thanks for the reply,
I had figured it out and forgot about this open question.
The steps to derive at the formula are:
- Use Bienaymé’s identity for the variance of the mean
- Transform it to get something like: Var(\hat{\mu}) = Var(S)\tau_t/N
- Identify the term for the autocorrelation at lag t , i.e. \tau_t
- Take the limit N \rightarrow \infty and assuming that the sum over the correlations is ‘absolutely summable’ (see Cesaro sum), one gets \tau_t \approx 1+2 \sum^{\infty}_{t=1} Corr(X_i, X_{i+t})
Definitions:
- \hat{\mu}: estimate of mean value
- S: sample of X_i, ..., X_N values
- N: number of sampling points