7 Forecasting non-stationary time series

In chapters 4, 5, and 6, we covered the moving average model or MA(q), the autoregressive model or AR(p), and the ARMA model or ARMA(p,q). We saw how these models can only be used for stationary time series, which required us to apply transformations, mainly differencing, and testing for stationarity using the ADF test. In the examples that we covered, the forecasts from each model returned differenced values, which required us to reverse this transformation in order to bring the values back to the scale of the original data.

Now, we introduce another component to the ARMA(p,q) model to forecast non-stationary time series. This component is the integration order, which is denoted by the variable d. This leads us to the AutoRegressive Integrated Moving Average model or ARIMA(p,d,q). Using this model, we can take into account non-stationary time series and avoid the steps of modeling on differenced data and having to undifference the forecasts.

7.1 Defining the autoregressive integrated moving average model

7.2 Modifying the general modeling procedure to account for non-stationary series

7.3 Forecasting a non-stationary times series

7.4 Next steps

7.5 Exercises

7.5.1 Medium: Apply the ARIMA(p,d,q) model on the datasets from chapters 4, 5 or 6.

7.6 Summary