Image by Elijah Grimm In this article we will cover the ARMA and ARIMA based statistical models, cover the maths behind these models, and look at the statistical test required prior and the post the model fitting. I’d recommend reading the previous article here before reading the remainder of this article. In that article we cover the basics of what is a time series and how we could model it. Definitions: Recall from our previous article that given a sequence of data points $\{ X_{t}, t \in \mathbb{Z} \}$, the sequence is strongly stationary or strictly stationary if