I am working on a problem where I have to first classify whether a time-series is periodic or not and then, if it is periodic identify its period(s) (the time-series could have multiple periodicities, also).
I need a reliable approach to say that a time-series is not periodic. I have been searching about this topic and these are some leads:
- Low values in the autocorrelation function (this leads to missing some multi-periodic time-series). Based on section 3.2 of the paper Characteristic-Based Clustering for Time Series Data.
- The time-series values are Gaussian and its power spectral density is exponential (this also leads to missing time-series with periodicities). Based on section 5.1 of the paper Identifying Similarities, Periodicities and Bursts for Online Search Queries.
Are there some other properties of time-series that can be used?