Today's "progress"

What have I managed today, to justify my existence? Apart from a picture frame falling in the wind and shattering (just as I'd made a breakthrough in my programming), it's been pretty uneventful.

I'm still looking into methods to uncovering structural breaks in datasets. In particular, multivariate data-sets. In single equation work, much has already been done in this area by my supervisor, David Hendry, and another of his students, Carlos Santos. It's struck me it would be great to be able to use this procedure in the cointegration space. In a cointegrated VAR model, it's the cointegration space that contains the stationary relations in the data, or the near-stationary relations. In effect, they're not different to simple univatiate equations, but certainly the statistical properties of any estimating and testing procedure are much more complicated.

So up to now I've been coding up programs in Ox to firstly estimate cointegrated VAR models using Reduced Rank Regression, and then testing restrictions on these models. The predominant method appears to be likelihood ratio tests, but so far my results suggest that actually, this test is somewhat over-sized, albeit having good power as a result.

Of course, there are about ten billion issues involved here, not least the cointegration rank - if one puts in a shift dummy, then things will look much more stationary, because a lot of non-stationary processes look stationary with a structural break. So one thing would be to test across a range of rank choices possibly. One may underselect the rank because a big structural break occurs in one cointegrating vector, one (otherwise) stationary combination, making it hard to spot using the Trace test.

But how does this link to my faith? And why should it?

How? Well I'd like to enable people to more accurately model processes through using shift dummies and other deterministic terms so that a better understanding of the world we have been given might be discovered. God has provided us with an immensely complicated world, in which it is very hard to gain any genuine understanding of what is actually happening. I think this is different in the physical sciences, but I'm no physical scientist.

In econometrics, it is generally posited that there exists some "data generating process", a DGP. I hold to this view, and fully believe all these generating processes are given by God, set in place by Him in His creation, for us to understand more of. However, it is impossible to ever know one has stumbled across this DGP when carrying out econometric analysis. Nevertheless, if one has fitted a statistical model to a set of data, just like if one fits a t-shirt to one's self, there are ways to tell if the model (or t-shirt) fits. These ways are statistical tests, tests that the assumptions underlying the statistical model are upheld in the data. If one is able to find that these tests are all passed, then that is a good sign that good inference is being made on the data and (hopefully) the economy.

However, faced with the complexity of the economy, and the difficulties of econometric data and models, a lot of people throw their hands up about econometrics, and focus simply on the theory instead, describing very nice models with complicated mathematics, which tell essentially the story they like to think about the economy. I'm not particularly happy about this; it seems a bit like the person saying everyone has their own truth and that's ok. Except it's not. If there is a DGP underlying the economy, but people think up nice models that perform nothing like the real economy, and then give policy prognosis based on these, this is possibly dangerous.

So I'd like to think a better way is to think about how instead one might better understand the economy from looking at the data. One particular issue is that of structural breaks. Everyone knows the world changes. It wasn't like it is today 300 years ago. So one convenient assumption that theorists make, that the world is stationary, is clearly untenable.

But it's one thing to know a structural break occurs, it's another to correctly account for it, using a shift dummy or something. When exactly did it occur? And then, you might not even notice the break occurs. You might not know how many occured.

So summing up, I'm looking at how these structural breaks can be accurately detected, in order that better inference might be made on the economy through better statistical models that closely capture the "truth" out there. A "truth" put into place by God.

But why should this link to my faith? When challenged about what one should do before God to obey Him and get right with Him, Jesus replied " 'Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment." (Matthew 22:36-38). Thus it is right that with all my mind I love God, or at least try to. My work shouldn't be a time when I'm not worshipping Him.

Right, it's 3pm, and that program is still not working properly, so enough for now...