I thought I understood all of the examples in the text, but now I am very confused. Looking at the 3 month T Bills, trying to get a handle on what NEAS did. The sample autocorr function for the yt series leads me to take first differences. Fine. The sample autocorr function for the first differences goes toward zero quickly and Bartlett's confirms that this is good, so I would go with AR(1). I have no idea how to get the coefficients? I'm pretty sure, based on the book, my own understanding and the posts here, that we would need to regress on the first differences. I would get that series, make predictions with it, then add up those predictions to get a prediction for the original yt (I'm not there yet, so that is a little hazy). But it doesn't make sense to fit a regression to the first differences, since they are just basically hanging out and alternating around zero. Which is what they should be doing - indicating stationarity. But you can't get a good fit to data like that. Am I right? What am I missing? Regressing on the original yt gives a nice fit, because it is a nicely increasing series. Not stationary, I know....
Can someone help me out with this?
Thanks!
Jacob: If interest rates are a random walk, are the first differences a white noise process? What model do we use, and what items do we use in the regression?
Rachel: If the interest rates are a perfect random walk, the first differences are white noise. The AR(1) model on the first differences gives a β of zero and an α equal to the drift of the interest rates. This is a perfect fit of the ARIMA model, with d = 1 and β = 0.
In practice, we don’t expect a perfect fit. We might have seasonality, or changing means, drifts, and variances. As the graph of interest rates on the NEAS web site shows, interest rates are complex and their pattern changes from time to time. Even if the ideal model is AR(1), the stochasticity makes the fit less than perfect.