I am new to time series analysis, and I amm trying to understand the concepts behind this analysis. But I am still confused about the methods used to do such analyss, and what is the difference between the decomposition of time series or using an ARIMA model.
Thank you in advance.
Time series decomposition generally involves partitioning a signal into seasonal, trend, residual and sometimes level, holiday etc. components, which assumes additive or multiplicative relationships. seasonal_decompose method in statsmodel.tsa library is a simple application of this. A more advanced version, which applies Box-Cox transformation beforehand automatically and accepts multiple seasonality frequencies, is mstl in R. Facebook's Prophet also employs seasonal decomposition in itself. And, usually, a ARMA model on residuals followed by a decomposition step is a typical approach in analysis.
In ARIMA, there isn't a decomposition of such type. It's a generalization of ARMA models, in which we first difference the series and fit an ARMA model. The differencing step is applied to make the signal more stationary, by eliminating trend and seasonality components. ARIMA models considering seasonality are called SARIMA, but it also doesn't involve decomposition.
