Modeling time series can become very complex; here, we will go through some of the most employed models one by one and explain some of the ideas behind them. We will start with the autoregressive model, continue with the moving average model, and finish off with the combined autoregressive integrated moving average model. To start off this section, import the statsmodel time series model framework:
from statsmodels.tsa.arima_model import ARIMA
The ARIMA function takes a Pandas time series and model parameters as input and sends back a model object. To use a combination of the decomposition and differencing method in order to make the time series stationary, I first removed the seasonal component broken out by the statsmodels function and then took the first difference and checked whether it was stationary:
is_stationary((carsales-carsales_seasonal).diff(1).dropna());
It is stationary—the ADF value is lower than the 5% critical value and p-value is smaller than...