a. Give an example of an economic time series that behaves like a white noise process.
b. Generate 100 observations from a white noise process which is normally distributed with zero mean and variance equal to 4. Compute the sample autocorrelation functions up to lag 10 and comment on their behavior.
c. Download the daily stock indexes for three U.S. industries from 2004 to the present. Plot the time series. Compute the autocorrelation functions of the indexes. Compute the returns to the indexes and their corresponding autocorrelation functions. Do you think that an MA process is appropriate to model the index returns? Propose an MA model and forecast 1-day, 2-day, 3-day, and 4-day-ahead index returns. Compute your forecast error, and a 95% confidence interval for your forecasts.