Granger causality and Intrade data.

 March 6, 2008 personal mathematics

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Granger causality is a technique for determining whether one time series can be used to forecast another; since the Intrade market provides time series data for political questions, we can look at whether political outcomes can be used to forecast other political outcomes.

There’s a library for the statistical package R to do the Granger test, and Intrade produces CSV market data. I fed the market data for various contracts since January 1, 2008 into R, and the output of that into GraphViz to make a nice-looking visualization; in particular, I connect a to b if a Granger-causes b with p -value less than 0.05. Darker arrows have smaller p -values. This is all an embarassing misuse of statistics and p -values, but it is quick and easy to do, and the results are fun to see.

Here is the graph for a lag of one day (i.e., does yesterday’s value of a predict today’s value of b ):

Here is the graph for a lag of two days (i.e., can the two previous days of data for a be used to forecast the next day of data for b ):

And here is the graph for a lag of three days:

Don’t take this too seriously. And one word of warning: an arrow from a to b does not mean that if a is more likely, then b is more likely—rather, it ought to mean that past knowledge of a can be used to forecast b . I suppose it would be interesting to add some color for the direction of the relationship, and maybe I’ll do that when I have another free hour.