exercises for Thu Mar 3

1. On Thu Feb 24 we spent time discussing general issues for prediction and prediction uncertainty, the general multinormal model, and Nils Exercises 9, 10, 11, 12, 13. We also started Ch 3, and will spend working time getting familiar with AR(p), MA(q), ARMA(p,q). So far our favourite serious model example have been versions of AR(1).

2. For Thu Mar 3, work with these. (i) In R, find the dataset called "nhtemp", annual temperatures at New Haven, from 1912 to 1971. Translate to Celcius!, then try a couple of models, including linear regression plus autocorrelation. Check whether the autocorrelation is significantly present. Give an estimate and 90 percent prediction interval for the NH temperature in 1972. (ii) Simulate n = 200 data points x_t from an AR(2) model with parameters (0.33,0.22), then try to estimate these values from your simulated data. Repeat the experiment say 100 times. (iii) Similarly simulate n = 200 data points from the MA(2) model, with parameters (theta_0, theta_1, theta_2) = (1, 0.44,0.33), and estimate these based on the simulated data.