Use the data in HSEINV.RAW for this exercise.(i) Find the first order autocorrelation in l...

Use the data in HSEINV.RAW for this exercise.

(i) Find the first order autocorrelation in log(invpc). Now, find the autocorrelation after linearly detrending log(invpc). Do the same for log(price). Which of the two series may have a unit root?

(ii) Based on your findings in part (i), estimate the equation log(invpct) β0 + β1Δlog(pricet) β2t + ut

and report the results in standard form. Interpret the coefficient and determine whether it is statistically significant.

(iii) Linearly detrend log(invpct) and use the detrended version as the dependent variable in the regression from part (ii) (see Section 10.5). What happens to R2?

(iv) Now use Δlog(invpct) as the dependent variable. How do your results change from part (ii)? Is the time trend still significant? Why or why not?