ECO521
Quantitative Methods II
Spring Semester 2023
Problem Set 3
These problems are due by the beginning of class, Wednesday, March 8, 2023. No
exceptions! You should submit a copy of the SAS program you wrote in order to solve
the problem, the output and any relevant charts, and of course your analysis of and solution
to the problem.
Please follow the specifications for submitting the problems (posted separately). Failure to
do so will result in a 10 percent penalty on the problem set. I reserve the right to escalate
the penalty on future problem sets if you insist on failing to adhere to the specifications.
important deviation: In order to simplify grading, keep the charts and SAS output for
each series together. Thus, the basic plot for the first series should be followed by the
identification output for that series, then the estimation output, the RMSE for the forecast,
then the alternative model estimation (see below), its RMSE, and finally the two final charts.
late problem sets will not be accepted!
General note: You are not required to use the DDE method to bring the Excel data into
SAS. You can use the “import wizard” instead if you choose.
1. Once again, the Excel workbook on Blackboard contains three real-world time series
data sets.
A. Use SAS to plot each original data series before proceeding to the next phase of
analysis. State your impressions of each series before doing any identification or modeling
attempts.
B. Use SAS to obtain the SACF and SPACF for each series and tentatively identify a
time series model for each series. You must decide on one model — you may not hedge
your bets! If you insist on selecting multiple models, I will take the first identification you
make as your solution and will ignore the rest.
C. Detach the last 10 percent of the observations for each series. Now use
SAS to estimate the model that you identified. Discuss (based on the SAS output) how well
you were able to identify the model.
D. Use your model to forecast the observations you deleted from the full data set. (Of
course, the number of forecasts should match the number of observations in your holfdout
set.) Compute the RMSE for the forecast.
E. Now formulate a reasonable alternative model and use it generate a new pseudo
out-of-sample forecast and find the RMSE for the new forecast. Explain why you selected
the alternative model. Compare the RMSEs from the two forecasts. Which forecast seems
better? Note: Of course, you are doing this step for each series.
F. Finally, plot the actuals, fits, confidence band and forecast for each ARIMA forecast.
This includes the alternative forecasts. Be sure to clearly label the charts.