Prices of stocks are more appealing than returns in the sense of having a high R2 because prices suggest many more patterns [see Exercise 32, part (d)]. The time series in this exercise is monthly prices of shares in Exxon-Mobil from January 2000 through December 2011.8
(a) Fit a linear trend to this time series. The data table includes a column Month, which runs 1, 2, c , 144, to use as the time variable t. Does the trend capture the dependence over time, or does it leave substantial dependence in the residuals?
(b) Add two lags of the price to your model, so that the model includes the linear trend as well as Yt -1 and Yt -2. Remove any unnecessary predictors and summarize the ft of your model. Summarize the ft of you model.
(c) How has the slope of the time trend changed from that estimated in part (a)? Explain the reason for the change.
(d) Does the model chosen in part (b) meet the conditions for the MRM?
(e) Build a similar regression model using a linear time trend and lags of the response to predict the returns on Exxon-Mobil. Summarize the ft of the resulting model. Returns are the change in price divided by the price in the earlier period, (price t – price t -1) / price t -1.
(f) Compare using the models chosen in parts (b) and (e) for forecasting the price of stock in ExxonMobil next month. Which would you prefer to use (if either)? Explain your choice.

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