# TBATS decompostion and how to distinguish "real" sesonality

I am doing exploratory data analisis with TBATS decomposition, to get understand better seasonal patterns behind number of booking. One of my coworkers proposed that there is two weekly seasonality, because frenchmen get salaries every two weeks. I was using TBATS decomposition. However I noticed that no matter which argument I'll use in seasonal.periods, they will appear on graph with better and worse effect.

How do I figure out which seasonal periods are real?

In other case I was playing with time series of air temperature in Berno. To my suprise, TBATS detected weekly and monthly seasonal periods. If we think about it temperature should only have yearly and daily periods, maybe weekly due to human activity, but monthly?

Is that even legit?

• If you accept weekly periods due to human activity, then maybe monthly are related to salaries being paid? Mar 19, 2019 at 11:09

## 1 Answer

Note the comparisons between the vertical axes of your decomposition plots. The seasonal signals are tiny compared to the other signals and the noise. This earlier thread is closely related: Even after seasonality adjustment, seasonality still remains. Why?

Figuring out which seasonality is "real" is a bit of a philosophical question. As long as you don't create your data yourself, you don't know your actual data generating process.

If what you are looking for is good forecasts, then I suggest you run different models on holdout samples and use whatever yields the smallest holdout error. This may be a simpler model than the actual data generating process.

Conversely, if what you are looking for is understanding, then I don't think you can do much better than what I wrote in the first paragraph. Biweekly paycheck effects may have an impact... but I have looked for similar effects in retail sales, and I find them much more rarely than a nice narrative and story would suggest.