Forecasting with ARIMA models

The automatic method in the previous exercise chose an ARIMA(0,1,1) with drift model for the austa data, that is, \(y_t = c + y_{t-1} + \theta e_{t-1} + e_t.\) You will now experiment with various other ARIMA models for the data to see what difference it makes to the forecasts.

The Arima() function can be used to select a specific ARIMA model. Its first argument, order, is set to a vector that specifies the values of \(p\), \(d\) and \(q\). The second argument, include.constant, is a booolean that determines if the constant \(c\), or drift, should be included. Below is an example of a pipe function that would plot forecasts of usnetelec from an ARIMA(2,1,2) model with drift:

> usnetelec %>%
    Arima(order = c(2,1,2), include.constant = TRUE) %>%
    forecast() %>%
    autoplot()

In the examples here, watch for how the different models affect the forecasts and the prediction intervals. The austa data is ready for you to use in your workspace.

Plot forecasts from an ARIMA(0,1,1) model with no drift.
Plot forecasts from an ARIMA(2,1,3) model with drift.
Plot forecasts from an ARIMA(0,0,1) model with a constant.
Plot forecasts from an ARIMA(0,2,1) model with no constant.

Exercise

Forecasting with ARIMA models

Instructions