Well, I'm almost done. I have to figure out how to do two more things, then do them, and I'm all done.
So, my first series was easily modeled as AR(1). I tested the sample autocorrelations of the residuals from that regression, and they were definitely white noise. No real problem.
The problem has been my second series. AR(1) and AR(2) don't fit. Not for the rates, nor the first or second differences. So, I need to try an MA(1) and an ARMA(1,1) model. I have a friend using the same data, very similar periods, and her second series was an ARIMA(1,2,1), so I think I am on the right path. The hassle is that I don't know how to create those models! She used Minitab, which I don't have. I'm stuck re-reading through posts and the books, because apparently there is a 'long way' to create those models.
, I created a Word document as I worked through this, noting what I was doing (mostly to keep me from getting lost). It's 7-8 pages now. I think I did a good job on the project.
Anybody out there have advice regarding MA(1) or ARMA(1,1) models?
Jacob:
Should we assume that an AR(1) model works? Should we assume that we need a moving average component? Should we assume that Treasury bill and Treasury bond rates have different time series models? How do we know which is the right model? The textbook fits a complex ARIMA model; if we can’t do a nonlinear regression, how do we fit that model?
Rachel: The purpose of the student project is not to find the ideal model. No one knows the ideal ARIMA model for interest rates. The suggestion in the textbook is one model for one time period that might not work for another time period.
Jacob: If there is no clear solution, why are using these data?
Rachel: The purpose of the student project is to apply the time series concepts to real data. No model is ideal, and your results depend on the time period you choose. Choosing a time period that differs by a year or two may lead to a different model. The student project should show your hypotheses, your statistical tests, and your results. We are not looking for a specific answer.
Jacob: If AR(1) works for one time period, why doesn’t it work for another time period?
Rachel: Several explanations are possible:
In one period, the Federal Reserve Board targets a stable interest rate; in another period, the FED targets lower unemployment or higher GDP growth or lower inflation.
Twenty years ago, interest rates were influenced primarily by domestic factors. In the past decade, international competition and capital flows play a greater role.
Inflation, regulation, and markets have changed greatly over the years. Each of these affects the interest rate process.
The apparent difference may be spurious. Exogenous factors, like wars, elections, oil price changes, and recessions cause temporary changes in the ARIMA parameters.
Jacob:
If an AR(1) model fits for two eras, do we expect the same parameters?
Rachel: Of the three interest rate eras on the NEAS illustrative workbook, the first period has an upward drift and the third period has a downward drift. These give different autoregressive parameters.