How to do & plot simple and rolling linear regression on financial data xts object in R?

Question

Working with 30 minute data, of which I have put a sample online. It's the notional dollar value of the spread between ES and 2 contracts of NQ (ES-2*NQ). Sample is small, but should be long enough to use directly in a demo if you like. R code to grab it and use it as I am trying to:

demo.xts <- as.xts(read.zoo('http://dl.dropboxusercontent.com/u/31394273/demo.csv', sep=',', tz = '', header = TRUE, format = '%Y-%m-%d %H:%M:%S'))

head(demo.xts):

                        [,1]
2013-05-27 00:00:00 -37295.0
2013-05-27 00:30:00 -37292.5
2013-05-27 01:00:00 -37300.0
2013-05-27 01:30:00 -37280.0
2013-05-27 02:00:00 -37190.0
2013-05-27 02:30:00 -37245.0

What I am mainly after is a rolling window regression (or linear regression curve, as my trading platform terms it) - save it, then plot it. And, I figured to lead up to that I should be able to also plot a single simple regression for a specified time period. After the window regression, I would add standard deviation "bands" to that, but I think I can figure that one out later using TTR's "runSD" on the rolling regression. Sample of what I am after:

chart with hand drawn lines

I think this - Rolling regression xts object in R - got me the closest to what I think I am after. It seemed to work with my data, but I couldn't figure out how to turn the resulting "coefficients" into a line or curve in the notional dollar value plot I want to work with.

Referencing any package (like TTR) would be great; happy to load anything that makes this more simple or easy.

I can't figure out how the "standard deviation bands" would be calculated. Can you provide a formula? — Joshua Ulrich
@JoshuaUlrich the way i understand it it is the linear regression curve ± number of standard deviations times the price. so, using your sample code below, it seems like rma + 2*runSD(demo.xts, n=20) works to add the "upper band," for example. also, the other answer by vincent seems to come up with a similar result as expected with the "lwr" and "upr" that the predict function outputs. — Paul-s

Vincent Zoonekynd Vincent Zoonekynd · Accepted Answer · 2013-07-21T11:01:33

You can use predict to compute the points on the regression line and tail to extract the most recent one.

# Sample data
library(quantmod)
getSymbols("^GSPC", from="2009-01-01")

# Rolling regression (unweighted), with prediction intervals
x <- rollapplyr( 
  as.zoo(Ad(GSPC)), 
  width=300, by.column = FALSE, 
  FUN = function(x) {
    r <- lm( x ~ index(x) )
    tail(predict(r, interval="prediction"),1)
  } 
)

# Plots
plot( index(GSPC), Ad(GSPC), type="l", lwd=3, las=1 )
lines( index(x), x$fit, col="purple", lwd=3 )
lines( index(x), x$lwr, col="purple", lwd=3, lty=3 )
lines( index(x), x$upr, col="purple", lwd=3, lty=3 )
abline( lm( Ad(GSPC) ~ index(GSPC) ), col="light blue", lwd=3 )

Moving regression

How to do & plot simple and rolling linear regression on financial data xts object in R?

2 Answers