You are investigating the presence of day of the week effects in daily stock index returns. Using daily data for the Japanese equity market from January 2003 to December 2008 (a total of 1,495 observations) you estimate the following model, with t-ratios given below each estimated coefficient in parentheses:

Rt=-0.30 - 1.31MONt+1.47TUEt+0.79WEDt-0.01THUt
        -0.43   -2.29           1.75             (0.70)         (-0.02)

           

where R_t is the daily return on the Japanese equity index, MON_t is a dummy variable that equals 1 on Mondays and zero otherwise, TUE_t is a dummy variable that equals 1 on Tuesdays and zero otherwise, WED_t is a dummy variable that equals 1 on Wednesdays and zero otherwise and THU_t is a dummy variable that equals 1 on Thursdays and zero otherwise. Note: equity markets only trade during business days (i.e. Monday to Friday) and so there are no returns observed at weekends.

Interpret and discuss the estimated values of the regression coefficients on the dummy variables MON and WED. How would you interpret the estimated value of the (common) intercept term in this model?

Using the t-ratios given above, determine whether there is evidence of significant day of the week effects in Japanese equity index returns. Clearly explain how you reach your conclusion. If you had access to additional estimation results from the model above, is there any alternative way you could test for day of the week effects instead of using the t-ratios above?

Using two separate equations, write the estimated regression model that applies on Tuesdays and the regression model that applies on Thursdays.

Define the problem of measurement error in the context of linear regression models. Explain what the potential consequences of this problem are and briefly outline what potential solutions are available.