The file mdec5FF6117.

txt contains the monthly returns of the CRSP Decile 5 portfolio and the Fama–French factors from January 1961 to June 2017. The data are in percentages. The Decile 5 returns are from CRSP and have been adjusted by removing the risk-free interest rates. Fama–French factors are from Professor K. French’s website.

(a) Fit a linear regression model relating the Decile 5 excess returns to the Fama–French factors. Write down the fitted model and perform model checking.

(b) Fit a time-varying coefficient model relating the Decile 5 excess returns to the Fama–French three factors as shown in Example 6.2.

(c) Show the time plots of smoothed states using a diffused initial value.