Multiple linear-regression models expressed the variable of interest as a linear combination of predictors or input variables. Univariate time series models relate the value of the time series at the point in time of interest to a linear combination of lagged values of the series and possibly past disturbance terms.

While exponential smoothing models are based on a description of the trend and seasonality in the data, ARIMA models aim to describe the autocorrelations in the data. ARIMA(p, d, q) models require stationarity and leverage two building blocks:

• Autoregressive (AR) terms consisting of p-lagged values of the time series
• Moving average (MA) terms that contain q-lagged disturbances

The I stands for integrated because the model can account for unit-root non-stationarity by differentiating the series d times. The term autoregression underlines that ARIMA models imply a regression of the time series on its own values.

We will introduce the ARIMA building blocks, simple autoregressive (AR) and moving average (MA) models, and explain how to combine them in autoregressive moving-average (ARMA) models that may account for series integration as ARIMA models or include exogenous variables as AR(I)MAX models. Furthermore, we will illustrate how to include seasonal AR and MA terms to extend the toolbox to also include SARMAX models.