Description
Recall the dataset TempPG.csv from Lab 6, which includes minimum temperatures measured
at Prince George, BC, from 1919 to 2008.
You may have considered fitting an AR(1) model based on the inspection of the sample acf
and pacf for the annual minimum temperatures. In this lab, you will be guided to revisit the
AR(1) model and compare it to a competing model.
1. Fit the AR(1) model to the annual minimum temperatures using the arima()command,
and write down your fitted model.
2. Look again at the acf of the annual minimum temperatures. In what way does the acf not
behave as you would expect for the fitted AR(1) model?
3. Plot the series of first differences of minimum annual temperatures. Plot the acf and pacf
of the differences. What model would you suggest for the differences?
4. Fit the suggested ARIMA model to the annual minimum temperatures series. Write down
your fitted model.
5. Use the tsdiag() function to see diagnostic plots for the model you have fitted. How well
does the model appear to fit?
6. Recall the Akaike Information Criterion (AIC), defined to be (proportional to)
− log (maximum likelihood) + 2r,
where r is the number of independent parameters in the model.
This statistic can be used
for model selection. Models with smaller AIC values are often preferred. Compare the two
competing models here via their AIC values. Which model would you select?