Final Exam Review Eco 5375 Business and Economic Forecasting Fall 2011 Our final exam is on Wednesday December 14 3 00 6 00 PM in Room 351 Maguire 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 with the exam proctor You can use any calculators that do not have access to notes and the like We will also provide you with a 4 function calculator if you should need one I recommend that you review your notes your quick quizzes QQ7 QQ12 and your exercises EX8 EX11 since the mid term exam Of course the final exam is cumulative and therefore reviewing the notes QQs Exercises associated with the mid term as well as the mid term exam itself would be advised See the Midterm Review sheet that is posted on the class website for details Roughly 60 of the exam will be on the material since the mid term while the remaining 40 will be on the material covered before the mid term The Keys for the quick quizzes and exercises are posted on the course website The major new topics since the last mid term are as follows You should know the notation of the Multiplicative Seasonal BoxJenkins model and how to write out an estimated Seasonal Box Jenkins model as we did for the Plano Sales Tax Revenue data See the pdf file Seasonal Differencing pdf Important SAS programs in this context are Plano Unit 2 sas and Plano Multiplicative BJ sas Our crude 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 To pursue a more formal statistical approach to differencing 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 Also see Exercise 8 and the SAS program Plano Unit 2 sas We built a Multiplicative Seasonal Box Jenkins model for the Plano Sales Tax Revenue data and used it to forecast future Plano Sales Tax Revenue See Exercise 9 To come to understand the patterns in the ACF and PACF that occur with various Multiplicative Seasonal BoxJenkins models see the files season jpg season1 jpg 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 The Equal Lag Length VAR was discussed as a way of examining the usefulness of a supplementary variable in helping to forecast a target 1 variable For a beginning discussion on VARs see the file Vector Authregressions pdf that can be found on the class website I spent some time in class discussing an example of using the Yield Curve as a supplemental variable to predict future growth of real GDP as is frequently done by the Federal Reserve Bank of Cleveland See the Cleveland Fed website http www clevelandfed org research data yield curve index cfm and the pdf file Yield Curve GDP Growth Cleve Fed pdf in the notes subdirectory of the class website Recall the Series M data set that we discussed in class We used systemwide 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 10 for building an equal lag length VAR for the Series M data and conducting the out of sample forecasting experiment horserace between the BoxJenkins model and the RVAR model 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 10 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 significantly different in a statistical sense See my class notes Also see Exercise 10 for the application of the test and the SAS program M Horserace sas 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 11 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 null hypothesis of unbiasedness of a forecasting method See my class lecture notes on this issue If both forecasting methods are unbiased then the Nelson Combination Forecast method is to be preferred If one or more of the forecasting methods are biased then it is suggested that the Granger Ramanathan combination method be used 2