11. (i) Simulate n = 800 observations with a simple periodic function, a period of 100, and errors of form AR(3) given in exercise 4, choose the simple periodic function so that initially 0.75 < R2 < 0.95.

(ii) Fit a simple periodic function to the data and use the residuals to assess the order AR(m) and compute R2 for the model fit.

(iii) Average over 5-day periods, fit a simple periodic function to the data and use the residuals to assess the order AR(m) and compute R2 for the model fit.

(iv) Average over 10-day periods, fit a simple periodic function to the data and use the residuals to assess the order AR(m) and compute R2 for the model fit.

(v) Average over 20-day periods, fit a simple periodic function to the data and use the residuals to assess the order AR(m) and compute R2 for the model fit.

(vi) Summarize how the AR(m) order and R2 change as greater averaging is introduced.