2. Forecasting. For this problem, use file cambridge.dta. The file contains monthly means

of daily maximum temperature (variable maxtemp) in Cambridge, from January 1959 up to

September 2018. For example, in September 2018, the average maximum daily temperature in

Cambridge was 19.9 degrees of Celsius.

(a) Make a time series plot of maxtemp. Summarize the behavior of these time series. Plot

the correlogram of maxtemp. Comment.

(b) Run the regression of maxtemp on the month dummies (don't fall into the dummy variable

trap!). How would you interpret the coefficients? Save the residuals from this regression

as variable res.

(c) Make a time series plot of res. Any signs of global warming? Plot a correlogram of res.

Comment.

(d) Regress res on variable t, which indexes time, and a constant. Save the residuals as

variable res1. Plot a correlogram of res1. Compare with the correlogram of res. Can

you explain the difference?

(e) Estimate an AR(1) model for res1. Test hypothesis of no AR(1) serial correlation in the

errors of this model.

(f) Given your estimates in (b-e), what is your forecast of the mean daily maximum temper-

ature in Cambridge in February 2018?