# Granger causality and Intrade data.

##### 2008-03-06 19:31:09 +0000economicspersonalcomputersciencemathematics

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.