# TBATS: why set seasonal periods?

While trying to estimate the level, trend, and seasonal components with the TBATS model (forecast pkg in R), I notice that the plot of components of the time series does not include the seasonal component unless the frequency of the time series is specified explicitly.

On a fundamental level, my question, why is it necessary to specify the seasonal periods (or frequencies). Are there algorithms which determine the time periods by automatically (perhaps a Fourier model) which can then be combined with TBATS for accurate decomposition of components?

Why would you avoid specifying the seasonal frequency of your data if you know it? It will be easier and likely more reliable then making some automated procedure estimate it for you.

If you are not sure whether there is a seasonal pattern at a given frequency, you can try estimating a model with the seasonal component and another model without it. Then you would compare the properties of the two models and see which one fares better. (E.g. compare the AIC or BIC of the two models.)

I do not know of algorithms that would estimate the seasonal frequency for you, but I guess there must exist some. These kind of algorithms could have been used in automated procedures; one example where automated procedures could have been used is forecasting competitions with a large number of series to be forecasted (but that is just my guess). Perhaps knowing that could help you find one.

• If I knew the seasonal period, I would specify it. But many a times, you just have the time series, and one would expect the decomposition algorithm to identify the level/trend/seasonal components all by itself. As for different techniques which identify the periodicity, seems like there are aplenty. Thanks for your insight though. Nov 4, 2014 at 19:54

Why do most seasonal time series and forecasting algorithms presume that the seasonal period is (are) known? Here are a few reasons:

1. For most applications, seasonal cycle lengths are known. Retail sales exhibit intra-yearly and intra-weekly seasonality. In Islamic countries, they exhibit a known irregular seasonality connected with the Islamic calendar. Electric power demand exhibits intra-daily, intra-weekly and intra-yearly seasonality. All these are known, and in such applications, no other seasonalities make sense.

I have been active in forecasting for about ten years now, and I at least have never come across a paper, conference talk or use case where the length of the seasonal cycle(s) needed to be estimated.

2. Of course you can estimate seasonal cycle lengths. However, the problem is that there are enormously many possibilities, so your estimates - both of the seasonal cycle length(s) and of the coefficients of your model - will have a high variance. If you have a lot of data, this can work. But if you have enough data to reliably estimate seasonal cycle length, i.e., multiple cycles of each potential length, you will likely be more concerned about whether your data generating process has changed during your history.

That said, a frequency domain decomposition could be said to model seasonalities of unknown lengths, without explicitly estimating the lengths of these seasonalities.