STAT 804: 97-3

Assignment 2

1. Consider the ARIMA(1,0,1) process

   

   Show that the autocorrelation function is

   

   and

   

   Plot the autocorrelation functions for the ARMA(1,1) process above, the AR(1) process with

   

   and the MA(1) process

   

   on the same plot when and . Compute and plot the partial autocorrelation functions up to lag 30. Comment on the usefulness of these plots in distinguishing the three models. Explain what goes wrong when is close to .

2. The S command

   attach(`/home/math/lockhart/teaching/courses/804/datasets')

   will make a dataset influenza available. If you type

   ls(pos=2)

   you will see the data set for this question and the next two.

   The data consist of monthly counts of influenza cases over a 9 and a half year period. Fit an ARIMA model to the data.

3. Fit an ARIMA model for the Johnson and Johnson earnings per share data which is in the dataset earnings. There is 20 years of quarterly data.

4. Fit an ARIMA model for the data set called fake.

DUE: Friday, 31 October.