Subtraction Is Crazy

April 4, 2013
By

(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 the calculus.

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 symbolic formulæ the (infinitesimal) first-differences of a function, made a decent splash.)

definition of derivative

Jeff Ryan wrote some R functions that make it easy to first-difference financial time series.

image

Here’s how to do the first differences of Goldman Sachs’ share price:

require(quantmod)
getSymbols("GS")
gs <- Ad(GS)
plot(  gs - lag(gs)  )

image

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:

image

Not perfectly similar, but very close!

Looking at the first differences compared to a Gaussian brings out what’s different between public equity markets and a random walk. What sticks out to me is the vol leaping up aperiodically in the $GS time series.

I think I got even a little closer with drawing the stdev’s from a Poisson process plot(rnorm(1570, sd=rpois(1570, lambda=5)), type="l")

image

but I’ll end there with the graphical futzing.

What’s really amazing to me is how much difference a subtraction makes.

To leave a comment for the author, please follow the link and comment on their blog: isomorphismes.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Sponsors

Mango solutions



RStudio homepage



Zero Inflated Models and Generalized Linear Mixed Models with R

Quantide: statistical consulting and training



http://www.eoda.de







ODSC

ODSC

CRC R books series











Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)