Subtraction Is Crazy

(This article was first published on isomorphismes, and kindly contributed to R-bloggers) I was re-reading Michael Murray’s explanation of cointegration: and marvelling at calculus. Calculus blows my mind sometimes. Like, hey guess how much we can do with subtraction. — protëa(@isomorphisms) March 28, 2013 Of course it’s not any subtraction. It’s subtracting a function from a shifted version of itself. Still doesn’t sound like a universal revolution. (But of course the observation that the lagged first-difference will be zero around an extremum (turning point), along with analytic methods of calculating the (infinitesimal) first-differences of a function, made a pretty big splash.) Jeff Ryan wrote some R functions that make it very easy to first-difference financial time series. Here’s how to do the first differences of Goldman Sachs’ share price: require(quantmod) getSymbols("GS") gs <- Ad(GS) plot( gs - lag(gs) ) Look how much more structured the result is! Now all of the numbers are within a fairly narrow band. With length(gs) I found 1570 observations. Here are 1570 random normals plot(rnorm(1570, sd=10), type="l") for comparison: Not perfectly similar, but very close! Looking at the first differences compared to a Gaussian is also a nifty way to show what’s different between public equity markets [...]