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@jstults jstults/os_stats.R
Created Jun 2, 2012

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simple time-series analysis of android market share data
OS Dec 2009 Jan 2010 Feb 2010 Mar 2010 Apr 2010 May 2010 Jun 2010 Jul 2010 Aug 2010 Sep 2010 Oct 2010 Nov 2010 Dec 2010 Jan 2011 Feb 2011 Mar 2011 Apr 2011 May 2011 Jun 2011 Jul 2011 Aug 2011 Sep 2011 Oct 2011 Nov 2011 Dec 2011 Jan 2012 Feb 2012 Mar 2012 Apr 2012
Android 5.2 7.1 9 10.3 12 13 14.9 17 19.6 21.4 23.5 26 28.7 31.2 33 34.7 36.4 38.1 40.1 41.8 43.7 44.8 46.3 46.9 47.3 48.6 50.1 51 50.8
RIM 41.6 43 42.1 41.7 41.1 41.7 40.1 39.3 37.6 37.3 35.8 33.5 31.6 30.4 28.9 27.1 25.7 24.7 23.4 21.7 19.7 18.9 17.2 16.2 16 15.2 13.2 12.3 11.6
Apple 25.3 25.1 25.4 25.2 25.1 24.4 24.3 23.8 24.2 24.3 24.6 25 25 24.7 25.2 25.5 26 26.6 26.6 27 27.3 27.4 28.1 28.7 29.6 29.5 30.2 30.7 31.4
MS 18 15.7 15.1 14.4 14 13.2 12.8 11.8 10.8 9.9 9.7 9 8.4 8 7.7 7.5 6.7 5.8 5.8 5.7 5.7 5.6 5.4 5.2 4.7 4.4 3.9 3.9 4
Smartphones 39.4 42.7 45.4 46.8 48.1 49.1 49.9 53.4 55.7 58.7 60.7 61.5 63.2 65.8 69.5 72.5 74.6 76.8 78.5 82.2 84.5 87.4 90 91.4 97.9 101.3 104.3 106.3 107.3
#
# 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 Dec 2009 Jan 2010 Feb 2010 Mar 2010 Apr 2010 May 2010 Jun 2010 Jul 2010 Aug 2010 Sep 2010 Oct 2010 Nov 2010 Dec 2010 Jan 2011 Feb 2011 Mar 2011 Apr 2011 May 2011 Jun 2011 Jul 2011 Aug 2011 Sep 2011 Oct 2011 Nov 2011 Dec 2011 Jan 2012 Feb 2012 Mar 2012 Apr 2012
Android 2.05 3.03 4.09 4.82 5.77 6.38 7.44 9.08 10.92 12.56 14.26 15.99 18.14 20.53 22.93 25.16 27.15 29.26 31.48 34.36 36.93 39.16 41.67 42.87 46.31 49.23 52.25 54.21 54.51
RIM 16.39 18.36 19.11 19.52 19.77 20.47 20.01 20.99 20.94 21.9 21.73 20.6 19.97 20 20.09 19.65 19.17 18.97 18.37 17.84 16.65 16.52 15.48 14.81 15.66 15.4 13.77 13.07 12.45
Apple 9.97 10.72 11.53 11.79 12.07 11.98 12.13 12.71 13.48 14.26 14.93 15.38 15.8 16.25 17.51 18.49 19.4 20.43 20.88 22.19 23.07 23.95 25.29 26.23 28.98 29.88 31.5 32.63 33.69
MS 7.09 6.7 6.86 6.74 6.73 6.48 6.39 6.3 6.02 5.81 5.89 5.54 5.31 5.26 5.35 5.44 5 4.45 4.55 4.69 4.82 4.89 4.86 4.75 4.6 4.46 4.07 4.15 4.29
Total 39.4 42.7 45.4 46.8 48.1 49.1 49.9 53.4 55.7 58.7 60.7 61.5 63.2 65.8 69.5 72.5 74.6 76.8 78.5 82.2 84.5 87.4 90 91.4 97.9 101.3 104.3 106.3 107.3
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jstults commented Jun 2, 2012

Here's the plot that this script makes.

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jstults commented Jun 2, 2012

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

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