Instructions: Show your answers in details.
The following question is given for the graduate students only!
Q4 (2 points): Quarterly earnings per share for the Johnson & Johnson Company are given in the data file named jj. The earnings per share data, say yt, covers the years from 1960 through 1980. In this problem, you are going to fit a special type of structural model, xt = log(yt), where xt = Tt +St +Et, where Tt is a trend component, St is a seasonal component, and Et is error (noise) term. Note that the time t is in quarters (1960.00,1960.25,···) so one unit of time is a year. 1. Fit the regression model
xt = βt +α1Q1(t) + α Q2(t) + α Q3(t) + α Q4(t)+ wt
|{z} | {z } |{z} trend seasonal noise
where Qi(t) = 1 if time t corresponds to quarter i = 1,2,3,4, and zero otherwise. The Qi(t)’s are called indicator variables. We will assume for now that wt is a Gaussian white noise sequence.
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