3. Consider the monthly simple returns of the Decile 1 (CAP1RET in the data file), Decile 2 (CAP2RET in the data file), Decile 9 (CAP9RET in the data file), and Decile 10 1

(CAP10RET in the data file) of U.S. stocks based on market capitalization. The data span is from January 1970 to December 2008. The data file is m-deciles08.txt (uploaded in the Problem Set folder in Canvas). (a) For the return series of Decile 2 and Decile 10, test the null hypothesis that the first 12 lags of autocorrelations are zero at the 5% level. Draw your conclusion. (b) Build an ARMA model for the return series of Decile 2. Check the estimated model. Is the estimated model a good/adequate model? Write down the estimated model. (c) Use the estimated ARMA model to produce 1- to 12-step-ahead forecasts of the series and the associated standard errors of forecasts.