for more details have a look at this section:
https://www.otexts.org/fpp/8/9
Hi,
It is true that, sometimes, ARIMA models can capture a little bit of seasonality, but it still be insufficient against strongly seasonal data.
However, even SARIMA can't capture the seasonality as well as periodic models does. Indeed, Tiao & Grupe (1980) has shown, mathematically, the superiority of periodic ARMA while dealing with seasonal time series.
You can estimate Periodic-ARMA parameters using Kalman Filter, Vecchia filter and Boshnakov's reccursions.
Best regards
TBATS and facebook's prophet can be used as good models to capture multiple seasonalities in the series
SARIMA can work correctly and product good results if you provide proper input of seasonality. this can be done by fourier (FFT) transform which is the most accurate of all transforms. It will give you the seasonal frequency as an output and you can transform it.
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