Again, consider the three-dimensional log returns of Problem 1. Fit a \(t\)-copula model with marginal Student \(-t\) innovations to the data. White down the fitted model and compute the resulting time-varying correlations.

Data from Problem 1

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.

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

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.