Jacob: The other postings give the considerations and techniques for the student project. What are possible topics for the student project?

Rachel: The student projects are of several types: fitting a model, comparing two or more time series, or applying a technique.

Jacob: What does a student project on fitting ARIMA models consist of?

Rachel: One type of student project fits an ARIMA model to a time series. We first graph the time series and select a time period that seems stationary or homogeneous non-stationary. We suggest eras in other postings.

The student project considers four types of ARIMA models: AR(1), MA(1), AR(2), and ARMA(1,1). For each of these, we consider both the interest rates themselves and the first differences, and we consider seasonality. This gives 4 × 2 × 2 = 16 potential models.

Jacob: Do we form 16 models?

Rachel: We test for stationarity and seasonality to determine if we use first differences and a 12 month seasonal lag. We then try an AR(1) model and use diagnostic testing to see if it fits well. We can if it fits well, we are done; if it does not fit well, we try one of the other three models. If the student project shows you know how to fit a model, you need not repeat the fitting work, but you should explain how you would fit the other models.

Jacob: What would a student project doing comparisons consist of?

Rachel: You can compare a short rate and a long rate, showing the differences in ARIMA parameters, seasonality, and autocorrelations. You can compare nominal interest rates and real interest rates, or interest rates and interest rate futures. You can compare the three eras in the post-World War II period.

Jacob: What would a student project on a technique consist of?

Rachel: We discuss five ways of adjusting for seasonality in another posting. You can compare these five methods.

Jacob: When doing a student project on comparisons, do we just show the techniques?

Rachel: The comparison must show the goodness-of-fit tests using each technique. For each technique, we form the correlogram of the residuals and see which technique leads to white noise. Sometimes more than one technique works well; sometimes no technique works well.