1 Final Exam Review Eco 5375 Business and Economic Forecasting Fall 2010 Our final exam is scheduled for Wednesday, December 8, 6:30 – 9:30 PM in Room 303 Lee. It is a closed notes test and thus you are not to have any notes in any form open during the test. Also you must check your phones and calculators with the exam proctor. If you need to do any calculations during the exam, we will provide you with a 4-function calculator for your use. This test is going to be comprehensive with approximately 1/3rd of the test containing material from the Mid-term review sheet and the rest coming from the topics referred to in this review sheet. Since the midterm we have covered the material indicated by QQs 7 though 16 and Exercises 9 through 15. The Keys for the quick quizzes and exercises are posted on the course website. The major topics we have covered since the mid-term are roughly the following: - The phenomenon of Spurious Regression in time series analysis especially as it relates to correlating one time series with another time series. For a Monte Carlo program that demonstrates the spuriously high correlation when you correlate two time series that have unit roots in them, see the SAS Monte Carlo program “spurious.sas.” - How to use the Augmented Dickey Fuller test to test for the presence of a unit root in a time series, and thus to determine whether to difference the data before building a Box-Jenkins model for it. You should know the different cases of the ADF test and when to use them. Also you should know their null and alternative hypotheses and what to do when you get a p-value that is either greater than or less than 0,05. See the documents “ADF Lecture Notes.pdf” and “ADF Notes.pdf” on the course website. See Exercise 9. - How to use the %Logtest Macro in SAS to determine whether to take the natural log of the data or not and how to produce forecasts of the original series when the data has been logged. See Exercise 10. - Our Box-Jenkins way of detecting seasonality was through the lens of the autocorrelation function and its behavior around the seasonal lags. See the document “Seasonal Differencing.pdf.” - We looked at the Hasza-Fuller and Dickey-Hasza-Fuller seasonal unit root tests to determine how to difference seasonal data to achieve stationarity. See the documents “Seasonal Differencing.pdf” and “Seasonal Unit Root Test Tables.pdf.” See Exercise 11. - We built a Multiplicative Seasonal Box-Jenkins model and used it to Plano Sales Tax Revenue data. See Exercise 12. To come to understand the patterns in the ACF and PACF that occur with various Multiplicative Seasonal Box-Jenkins models see the files season.jpg, season1.jpg –2 season10.jpg. Season10.jpg contains a summary “pattern” table for Multiplicative Seasonal Box-Jenkins models. All of these files can be found in the “season” subdirectory of the class website. - We went through building a time series models using the Unobservable Components modeling approach. See the document “Unobservable Components Model.pdf.” Also see Exercise 13. - The Equal-Lag-Length VAR was discussed as a way of examining the usefulness of a supplementary variable in helping to forecast a target variable. Recall the Series M data set that we discussed in class. We used system-wide goodness-of-fit criteria and PROC VARMAX to build the equal lag length VAR models for our out-of-sample forecasting experiments. We also built a Restricted VAR based on the information conveyed in the Granger Causal tests that we conducted on the Series M data set. See Vector Autoregressions.pdf and my class notes. See Exercise 14 for the horserace between the Box-Jenkins model and the RVAR model in the Series M data set. - The Granger Causality test was discussed in class as a way of determining if there might be a potential gain from forecasting with a Restricted VAR as compare to an Unrestricted VAR. See my classroom notes and Exercise 14 for an example of Granger Causal testing applied to the M data set. - The Diebold-Mariano test was discussed as a way to determine if the forecasting accuracies of competing forecasting methods are statistically significant. See my class notes. Also see Exercise 14 for the application of the test. - Finally we finished up the semester with a discussion of combination forecasting and in particular the Nelson Combination Forecasting Method and the Granger-Ramanathan Combination Forecasting Method. See Exercise 15 and Combo.sas for a presentation of this approach. The theory of combination forecasting is discussed in the document “Combination of Forecasts.pdf.” Recall that we discussed the Mincer Prediction-Realization diagram and the 45-degree line that indicates the unbiasedness of forecasts. One can generate an F-statistic for testing the unbiasedness null hypothesis. See my class lecture notes on this issue. If both forecasting methods are unbiased then the Nelson Combination Forecast method is to be