This candidate uses the project template on sports teams to fit AR(1) AR(2), and ARMA(1,1) processes to the Washington Redskins NFL team. His findings are similar to those of most other student projects: the more complex models – AR(2) and ARMA(1,1) – have better in-sample goodness-of-fit tests and the simpler model – AR(1) – has the better out-of-sample goodness-of-fit test. He is surprised by this contrast, but it is exactly what we expect from the principle of parsimony. He writes:

"The ESS of our forecasts stands in direct contrast to all of our other reasonability checks in that the AR(1) model has the closest fit. Based on our tests we would have expected to have the ARMA (1,1) model to come in the closest. … The model that came the closest was the very one we would have expected to have the largest error."

Don’t forget to check the accuracy of the forecasts in your student project. Bartlett’s test, the Box-Pierce Q statistic, the Durbin-Watson statistic, the p-values of each model parameter, and all the other goodness-of-fit tests are methods to determine which model will forecast best. The out-of-sample test may be distorted by random fluctuations in the years chosen (the data points) for the forecasts, so even the out-of-sample test is not conclusive.

But the principle of parsimony is powerful. In most student projects, the more complex models have better in-sample goodness-of-fit tests and the simpler models have better out-of-sample goodness-of-fit tests.

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[NEAS: The candidate writing this student project took both the regression analysis and time series courses. He asked NEAS if he could do both student projects on sports won-loss records.

The candidate’s postings on the discussion forum and his homework assignments showed the NEAS faculty that he understood the statistical concepts. NEAS replied that he should

Separate student projects are required for each on-line course. But you can use the same data, which reduces the time needed to complete the student projects.

The daily temperatures project templates can also be used for both time series and regression analysis student projects.

If you use the same data for both student projects, be sure to provide complete analyses for each. For the time series student project attached to this posting, the candidate uses the Yule-Walker equations to fit an ARMA(1,1) model and to verify his AR(1) and AR(2) models, compares the implied autocorrelations for each process with the sample autocorrelations, and uses the models to forecast the last year of data.

This time series student project fits an ARIMA process to the Minnesota Twins won-loss record. The student project is a good template for your own work, for several reasons: