Sounds reasonable.

There's a great argument to be made for using the RIGHT data.  If you pick 'wrong' data, you're in for a hard time. 

NEAS, there's a tip for you.  Give us plenty of data in the future to choose from, and strongly suggest we use it.  Data that is easy to get stationary, and can be modeled with a low order model, makes this project a useful exercise vs. a huge pain. 

Not that we didn't have data provided this year, but I used my own data simply on a whim.  I didn't think it'd make a big difference.  It did.

Jacob: Why did NEAS choose these interest rate data?

Rachel: We chose the interest rate data for several reasons.

Jacob: Do you give all the interest rate histories on the web site?

Rachel: We give long (twenty year) and short (three month) Treasury yields, which had monthly auctions. We give the consumer price index, both seasonally adjusted and non-seasonally adjusted, to compute real interest rates. We give Moody’s high grade corporate bond yield, which varies daily.

Jacob: Why not give us all the rates and let us choose which ones we use?

Rachel: If we gave all the rates, some candidates would spend hours (or days) analyzing them all and deciding which to use.

Jacob: What if we want to use other interest rate series? Can we do so?

Rachel: You can find interest rate histories on dozens of web sites. You can use any interest rate history you want. Our concern is how you apply the statistical techniques, not the interest rates you use.

MA component--at first I didn't think the first-differenced series' sample correlogram shows MA component (naively buying into the project pdfs: "...most series are AR..."), or, I didn't want to believe its existance because of the work involved.  However, the sample correlogram did cross zero at lag 4 or 5, which matches well to the textbook's fitted model (though our time periods are slightly off) of ARIMA (8,1,4).

AR even order--yes, oscillating.

I used all three tests (Durbin-Watson, Bartlett's, and Box-Pierce's Q).  I also used 40 lags instead of 15 suggested by Tuba.  But it didn't make a difference for my model fitting, anyway.  AR(1) didn't work, nor did AR(2), and I know the order for MA is about 4 or 5.  So, that's my conclusion.

Playing devil's advocate here, but...

How do you know an MA component is there?

How do you know the AR term is even (oscillating, I am guessing?)

My experience so far, weak as it has been, is that it's hard to determine if there actually is an MA component. 

Plus, from what I remember of that example, the simpler models were still decent, they just kept checking to try to improve it.  If you wanted to, you could just check the simple models and see if any of them is at least acceptable. 

But you're probably just fine doing exactly what you're doing, and you shouldn't listen to me.

Just reread your first post, I see you already tried the simpler models.

If you don't mind my asking, what test stats did you use?  I'm assuming DW, Q, and Bartlett's on the pk's of the regression residuals, and by significant you basically mean that the residuals are proven to not be just white noise.

It is time to answer my own question...the textbook fit the 1960 to 1996 3-month T-bill rate series to a bunch of models and ended up with ARIMA (8,1,4) in example 18.1.  So, the 1945-1978 series can't be that far from the 1960-1996 series, wouldn't we say?  I now know two things from the sample correlogram (of the first-differenced series):

1.  MA component is definitely present;

2.  AR component's order is an even number. 

So, there is room for errors in my calculation, but by and large, the textbook's example affirms that none of the simple models we are asked to fit in the student project--AR(1), AR(2), MA(1), MA(2), ARMA(1,1), etc.--would work.  And that'll be my conclusion in the write-up. 

OK, I used Moody's, so I won't take up much time and space here, but here's a good question:

What do you mean by 'significant', when you refer to the test stats?  It is possible that you're doing the checking wrong, or something like that. 

I mean, if your correlogram looks good, and your data 'passes' the Q statistic and the Bartlett's formula things decently well, the regression should work okay.  I don't think that we're supposed to even have to deal with AR(2), let alone a more involved model, based on things I've seen in the NEAS posts.

Did you try matching forecasts, rather than relying on any tests?  Maybe that will make your fit look better than it is.

I am looking for those who use this series on their project (either still in progress or finished)--what model did you find best fit?  Obviously we have to first-differenced the series, then I see a clear geometrically declining and oscillatory sample correlogram, which I infer an AR with order greater than 1 would work.  I tried AR(1) first, of course the test stats came back significant; then I tried AR(2) in two ways--run the Excel add-in with 2 lag and using the textbook equations 4.3, 4.4, and 4.5--yet the test stats still came back significant.

Since this project is quite involved, I might have made some mistakes somewhere on my worksheets.  All my correlograms stop at lag k=40, maybe that's not enough for 408 data points? 

Any help is greatly appreciated.

If 4 to 7 sample autocorrelations are outside the 95% confidence interval, we examine lags 56 to 105. We may have a white noise process with minor distortions. The ARIMA model may be reasonably good, even if it is not perfect.