I have multiple samples of a time series (for example, the time series might be minutely samples from 12am to 3pm, and I have that for ten different days) and I'd like to compute the autocorrelation function $\rho(k)$ together with confidence intervals.
I can think of two "obvious" things to do:
- Chain all of the samples together end-to-end and compute the autocorrelation function and confidence intervals for the combined sample.
- Compute the autocorrelation function for each sample individually. Average the values pointwise to get the total autocorrelation function, and apply a square root rule to get the confidence intervals.
Both of these have disadvantages. Option (1) will have artifacts from where I have joined together the time series, which will become more import as I compute $\rho(k)$ for large $k$. Option (2) seems too ad-hoc - I wouldn't know whether to believe my confidence intervals.
Is there a canonical or correct way to do this?