Consider the monthly log returns of Fama bond portfolio (6 months), S&P composite index, and Procter & Gamble stock from January 1962 to December 2011 for 600 observations. The simple returns are from CRSP and given in the file m-bndpgspabt . txt. The three return series used are in columns 2,5 , and 6 . We shall use log returns. Since the bond returns have serial correlations, we employ an \(\operatorname{ARIMA}(1,0,8)\) model to filter the series. In addition, the scale of bond returns is much smaller so that we use percentage bond returns. The resulting data are in the file m-bndpgsp-6211.txt.

(a) Is there conditional heteroscedasticity in the three-dimensional log return series? Why?

(b) Apply the EWMA method with smoothing parameter \(\lambda=0.96\) to obtain time-varying correlations of the data. Obtain the sample means of the correlations.