a) Refit the AR(4) model of §4.6.3 to the annual mean global temperature series, and using the…

a) Refit the AR(4) model of §4.6.3 to the annual mean global temperature series, and using the fitted model create a series of predicted values from t = 2 to the last value in the series (using Equation (4.24)). Create a residual series from the difference between the predicted value and the observed value, and verify that within machine accuracy your residual series is identical to the series extracted from the fitted model in R.

b) Plot a correlogram and partial correlogram for the mean annual temperature series. Comment on the plots.

c) Use the predict function in R to forecast 100 years of future values for the annual global temperature series using the fitted AR(4) model (Equation (4.24)) of §4.6.3.

d) Create a time plot of the mean annual temperature series and add the 100-year forecasts to the plot (use a different colour or symbol for the forecasts).

e) Add a line representing the overall mean global temperature. Comment on the final plot and any potential inadequacies in the fitted model.

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