os_stats.csv

os_stats.R

#
# do some simple time series analysis on smartphone os data
# data: http://www.catb.org/esr/comscore/
# commentary: http://esr.ibiblio.org/?p=4368
#

# this file has the market share percentages table 
osdata = t(read.csv("os_stats.csv",header=TRUE,row.names=1))
# this file has the raw userbase in millions 
osdata2 = t(read.csv("os_stats_2.csv",header=TRUE,row.names=1))

# fit an ar1 with drift; see http://www.stat.pitt.edu/stoffer/tsa2/Rissues.htm
# for why we use xreg this way to get useful predictions out of R's arima fits 
ar110 = arima(ts(osdata[,1]), order=c(1,1,0), xreg=1:length(osdata[,1]))
# no drift 
ar110nd = arima(ts(osdata[,1]), order=c(1,1,0))

# fit the raw user numbers 
ar110_2 = arima(ts(osdata2[,1]), order=c(1,1,0), xreg=1:length(osdata[,1]))
ar110nd_2 = arima(ts(osdata2[,1]), order=c(1,1,0))

# make predictions based on the various fits 
nahead=3
driftxreg=length(osdata[,1])+seq(1,nahead)
ar110p = predict(ar110,n.ahead=nahead,newxreg=driftxreg)
ar110pU = ar110p$pred + 2.0*ar110p$se
ar110pL = ar110p$pred - 2.0*ar110p$se
ar110ndp = predict(ar110nd,n.ahead=nahead)
ar110ndpU = ar110ndp$pred + 2.0*ar110ndp$se
ar110ndpL = ar110ndp$pred - 2.0*ar110ndp$se

driftxreg2=length(osdata2[,1])+seq(1,nahead)
ar110_2p = predict(ar110_2,n.ahead=nahead,newxreg=driftxreg2)
ar110_2pU = ar110_2p$pred + 2.0*ar110_2p$se
ar110_2pL = ar110_2p$pred - 2.0*ar110_2p$se
ar110nd_2p = predict(ar110nd_2,n.ahead=nahead)
ar110nd_2pU = ar110nd_2p$pred + 2.0*ar110nd_2p$se
ar110nd_2pL = ar110nd_2p$pred - 2.0*ar110nd_2p$se

# simulate a series from the drifting model 
totalxreg = c(0:length(osdata2[,1]),driftxreg2) 
nsims = 300
ar110_2sim = mat.or.vec(nsims,length(totalxreg)) 
for(i in 1:nsims){
  ar110_2sim[i,] = arima.sim(list(order=c(1,1,0),ar=ar110_2$coef[1]), n=length(totalxreg)-1, start.innov=ar110_2$residuals, sd=sqrt(ar110_2$sigma2)) + ar110_2$coef[2]*totalxreg
}

png("android_share.png")
plot(seq(0,length(osdata[,1])+nahead,length.out=10),seq(0,60,length.out=10),type="n",xlab="month",ylab="market share")
title(main="Android Market Share Prediction, AR1 w/&wo/drift")
points(osdata[,1])
lines(driftxreg, ar110p$pred[1:nahead], lty=1, col="darkblue")
lines(driftxreg, ar110pU[1:nahead], lty=2, col="darkblue")
lines(driftxreg, ar110pL[1:nahead], lty=2, col="darkblue")
lines(driftxreg, ar110ndp$pred[1:nahead], lty=1, col="darkred")
lines(driftxreg, ar110ndpU[1:nahead], lty=2, col="darkred")
lines(driftxreg, ar110ndpL[1:nahead], lty=2, col="darkred")
dev.off()

png("android_users.png")
plot(seq(0,length(osdata2[,1])+nahead,length.out=10),seq(0,60,length.out=10),type="n",xlab="month",ylab="users in millions")
title(main="Android Users Prediction, AR1 w/&wo/drift")
points(osdata2[,1])
for(i in 1:nsims){
  lines(ar110_2sim[i,2:33],pch=2,col=rgb(0,0,1,alpha=0.1))
}
lines(driftxreg2, ar110_2p$pred[1:nahead], lty=1, col="darkblue")
lines(driftxreg2, ar110_2pU[1:nahead], lty=2, col="darkblue")
lines(driftxreg2, ar110_2pL[1:nahead], lty=2, col="darkblue")
lines(driftxreg2, ar110nd_2p$pred[1:nahead], lty=1, col="darkred")
lines(driftxreg2, ar110nd_2pU[1:nahead], lty=2, col="darkred")
lines(driftxreg2, ar110nd_2pL[1:nahead], lty=2, col="darkred")
dev.off()

os_stats_2.csv

Here's the plot that this script makes.

New plot after typo fixed; confidence intervals overlap much more so next couple months will likely not be decisive.