In Exercise13.41, the regression assumption of Normality was checked. When the residuals exhibit non-Normality, a transformation of the response variable can sometimes rectify the issue.
(a) Take the logarithm of the trading volume data. Use software to fit a simple linear regression model using log(yt ) as the response variable and log(ytâˆ’1) as the explanatory variable. Record the estimated regression equation.
(b) Obtain the residuals from the AR(1) fit on the logged data. Make a histogram and Normal quantile plot of these residuals. In comparison to the Normality checks of part (c) of Exercise
13.41, howwell do these residuals match up with the Normal distribution?
(c) Use the fitted AR(1) model from part (a) to obtain a forecast for trading volume in logged units on December 23, 2008. Untransform the logged forecast to provide a forecast in the original units.