I was wondering if anyone could give me some insight on the relation between the ACF and the periodogram of a time series.
I have a bunch of timeseries and their ACF's and periodograms are typically much like the examples below.
For my analysis, I'm mostly interested in periodicity at lag 8 and 16 (for theoretical reasons)
The frequencies 'B' and 'HB' correspond to lag 16 and lag 8 respectively. The time series actually concerns interresponse intervals in musical performance of a piece that consists solely of eighth notes (16 of them in a 4:4 bar so 'B' stand for bar and 'HB' for half bar).
The thing I actually wanted to ask: in my periodograms, I consistently get very large peaks at frequency 0.25 (which corresponds to lag 4). However, the ACF peak at lag 4 is much smaller than those at lag 8 or 16. I was wondering how to interpret this finding. A lot of time series variance can be explained at this frequency even though the lag 4 autocorrelation is quite low?
I hope I was sufficiently clear in my question. If not, don't hesitate to ask me.