Consider the monthly log returns of CRSP decile portfolios 1, 2 , and 5 from January 1961 to September 2011.

(a) Specify a VMA model for the three-dimensional log returns.

(b) Estimate the specified VMA model via the conditional maximum likelihood method. Refine the model so that \(t\)-ratio of each estimate is greater than 1.645. Write down the fitted model.

(c) Use the fitted model to forecast the log returns of October and November of 2011 at the forecast origin September 2011. Obtain both the point and 95% interval forecasts.