How do you detect seasonality(multiplicative or additive) in a time series data?

Question

Trying to apply seasonal_decompose on timeseries data. It looks something like this:

            modal_price
Period  
2014-11-01  1469
2015-01-01  1258
2015-03-01  1112
2015-04-01  1373
2015-06-01  1370
2015-07-01  1406
2015-08-01  1520
2015-09-01  1860
2015-10-01  1436
2015-11-01  1455

Using freq=11 and seasonalcomponents are all Nan. What should i do in order to detect the seasonality type(multiplicative/additive) of this data?

Answer 1

Once divide the time-series by its Moving Average and once subtract the moving average from it.

If the seasonality is additive, then the result of subtract will have almost similar fluctuations in magnitude.

If it is multiplicative, then the division result has such a property.

Like the figures below from my course in Feature Engineering:

So the seasonality was multiplicative as the division has similar magnitudes of fluctuations.

Please note that more linear the dynamic of the time-series is, better this naive approach works.

Hope it helps!