Determine seasonal frequency from the values of the time series alone What are some algorithms for determining the seasonal frequency (or equivalently, the length of the seasonal period) from the values of the time series alone? That is, the values of the time series are given, but the time stamps are missing. However, we know the data has been sampled at equal time intervals.
(Further nuance could be added to the question, e.g. how this should be approached if our goal is to detect the "true" seasonal frequency vs. if our goal is to forecast the time series optimally under a given evaluation loss function. A motivating example for the latter case can be found here. A reference to an R implementation would be a bonus.)
 A: (cross-posted from here)
Section 3.2 in the following paper offers a possibility for determining the length of the seasonal cycle:
 Wang, X, Smith, KA, Hyndman, RJ (2006) "Characteristic-based
 clustering for time series data", _Data Mining and Knowledge
 Discovery_, *13*(3), 335-364.

However, this is only one aspect in a paper that is more comprehensive in its aims, so the specific issue of determining a seasonal length is not treated at great depth.
Also note that this was never included in the forecast::auto.arima() function (whose author is Hyndman), although this function does use other methods from that paper (for instance, auto.arima() decides whether to apply seasonal differencing for known seasonal cycle length based on an estimate of seasonal strength as also given in Wang et al.).
I do not now why this was never included. It may have been because it was unstable, varying and hard to automate. After all, you need to identify peaks and troughs in the ACF, and what constitutes a "peak" or a "trough" in a noisy ACF series would need to be operationalized.
Alternatively, perhaps there simply never was any demand for it, since users presumably know their seasonal cycle length.
So if you want to use the cycle length determination per Wang et al., you would need to code it yourself.
