These data measure hourly compensation in the US manufacturing sector from 1987 through 2011. The data are assembled by the Bureau of Labor Statistics from surveys. The value of the index was set to 100 in 2005, so the data indicate relative amounts not dollars. The data table includes a column Quarter, with consecutive values 1, 2,,.100, for modeling time trends.
(a) Fit a linear trend to summarize the pattern in these data. Would it be correct to describe the residuals as autocorrelated, or is there a better description of the pattern in the residuals?
(b) Form a dummy variable that takes on the value 1 in quarter 90 (the second quarter of 2009) and later. Add this dummy variable with its interaction with Quarter to the simple regression ft in part (a). Interpret the equation of the resulting multiple regression of compensation on Quarter, Dummy and Quarter * Dummy?
(c) Does the multiple regression estimated in part (b) meet the conditions of the MRM, or do problems remain?
(d) Consider a different way to model the response: its percentage rate of growth. Form the percentage changes in the compensation index and consider the timeplot of these. Does this series appear simple or do lags and time trends offer better forecasts?
(e) Which of these models would you use to forecast this time series? Justify your choice and use it to forecast the index for the first quarter of 2012. Include an interval with your forecast.