Consider the hourly \(\mathrm{PM}_{2.5}\) measurements of Station 2 (Column 5) in the data file TaiwanPM25.csv. Obtain the series \(y_{t}\) of the square-root transform of daily maximum \(\mathrm{PM}_{2.5}\). Reserve the last two years as the forecasting subsample.

(a) Entertain a scalar AR model for the \(y_{t}\) series. Compute the root mean squared errors of the 1-step ahead predictions of the AR model.

(b) Augment the predictors with the first six hourly \(\mathrm{PM}_{2.5}\) of each day. Compute the root mean squared errors of the 1-step ahead prediction using nowcasting. Is nowcasting helpful in this particular instance? Why?