#StackBounty: #time-series #clustering #seasonality #hierarchical-clustering Definition and Taxonomy of Seasonal Time Series

Bounty: 50

I want to

1. categorize a large number of time series into non-seasonal and seasonal
2. 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.

Get this bounty!!!

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