Download Project 1

Project Problem Set 1: Fitting a time series and detrending
Data Set: Usdata.xls
Problems
P.1 Using only the real GDP data for 1929 and 2005, and the geometric model, obtain an estimate for the
average annual growth rate for the U.S. economy.
P.2 Using only the real GDP data for 1929 and 2005, and the exponential, obtain an estimate for the
average continuous growth rate for the U.S. economy.
P.3 Show that, if you understand the relationship between annual compounding and continuous
compounding, you can calculate the continuous growth rate obtained in P2 from the annual growth
rate obtained in P1, and vice versa. Explain in words why the average annual growth rate is higher
than the average continuous growth rate.
P.4 Construct the constant growth rate time series path associated with your work above. (You should
get the same path for your work in P1 and P2.) Plot the model time series in the same diagram as the
actual real GDP time series, so that you can visually compare the model to the actual.
P.5 Run a regression to obtain a model path for real GDP using a first degree polynomial model. Present
your regression results in a professional manner, and plot the path predicted by the regression model
in the same diagram as the actual real GDP series, so you can visually compare the model to the
actual.
P.6 Run a regression to obtain a model path for real GDP using a first degree exponential model. Present
your regression results in a professional manner, and plot the path predicted by the regression model
in the same diagram as the actual real GDP series, so you can visually compare the model to the
actual. Comment on the size of the average continuous growth rate you obtain from this regression
model to that obtained when you only used the two data points for 1929 and 2005. Also, comment
on why the model path is different when you use regression.
P.7 Determine whether a second or third degree polynomial model fits better than the first degree model
you created earlier. If so, then present the regression results for your best fit model in a professional
manner, and plot the path predicted by the regression model in the same diagram as the actual real
GDP series, so you can visually compare the model to the actual.
P.8 Detrend the real GPD series by subtracting the model from the actual, for each model you have
created. Plot the different detrended series in one diagram. Comment on what the detrended series
are telling you about the U.S. economy?
P.9 Consider the following second degree exponential model: yt  Aer1t [1 / 2]r2t . Take the natural log
of this equation. Use your result to explain how you would use linear regression to find estimates of
r1 and r2 . Differentiate your result with respect to t. Use this final result to explain in words what
2
r1 and r2 represent.
P.10 Perform the regression you said you should perform in the previous question. Use your results to
determine whether there is evidence that the growth rate of the U.S. economy is changing over time.