Refer to Example 14.1 and the 2015 monthly IBM stock prices.
a. Use the exponentially smoothed series (with w = .5) from January to September 2015 to forecast the monthly values of the IBM stock price from October to December 2015. Calculate the forecast errors.
b. Use a simple linear regression model fit to the IBM stock prices from January to September 2015. Let time t range from 1 to 9, representing the 9 months in the sample. Interpret the least squares estimates.
c. With what approximate precision do you expect to be able to predict the IBM stock price using the regression model?
d. Give the simple linear regression forecasts and the 95% forecast intervals for the October-December 2015 prices. How does the precision of these forecasts agree with the approximation obtained in part c?
e. Compare the exponential smoothing forecasts, part a, to the regression forecasts, part d, using MAD, MAPE, and RMSE.
f. What assumptions does the random error component of the regression model have to satisfy in order to make the model inferences (such as the forecast intervals in part c) valid?
g. Test to determine whether there is evidence of firstorder positive autocorrelation in the random error component of the regression model. Use α = .05. What can you infer about the validity of the model inferences?