*Bounty: 50*

*Bounty: 50*

I want to

- categorize a large number of time series into non-seasonal and seasonal
- divide the seasonal ones into a small number of subgroups by type of seasonality

**Are there any formal definitions/taxonomies of seasonality out there?**

Or is this an "I know it when I see it" kind of phenomenon (to paraphrase Justice Potter Stewart)?

I don’t want to reinvent the wheel here, so I am curious if there is existing wisdom on how to do this well.

Here are a couple of off-the-cuff ideas:

- A simple concentration-index definition could be the sum of the

squared shares of the total for each time unit: $$sum_{t=1}^{T}

left(frac{y_t}{sum_{t=1}^{T}y_t} right)^2 $$When that sum exceeds some threshold, a series would be considered

seasonal. - A more complicated approach would be to decompose a time series into

trend, seasonal, cyclical, and idiosyncratic components and calculate

the fraction of total variation due to the seasonal part. A series

would be seasonal if that fraction exceeds some threshold. - The next step would be to cluster the shares or the seasonal components into groups that are similar.