Unit root, or not ? is it a big deal ?

[This article was first published on Freakonometrics - Tag - R-english, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Consider a time series, generated using

set.seed(1)
E=rnorm(240)
X=rep(NA,240)
rho=0.8
X[1]=0
for(t in 2:240){X[t]=rho*X[t-1]+E[t]}

The idea is to assume that an autoregressive model can be considered, but we don’t know the value of the parameter. More precisely, we can’t choose if the parameter is either one (and the series is integrated), or some value strictly smaller than 1 (and the series is stationary). Based on past observations, the higher the autocorrelation, the lower the variance of the noise.

rhoest=0.9; H=260
u=241:(240+H)
P=X[240]*rhoest^(1:H)
s=sqrt(1/(sum((rhoest^(2*(1:300))))))*sd(X)
Now that we have a model, consider the following forecast, including a confidence interval,
 
plot(1:240,X,xlab="",xlim=c(0,240+H),
ylim=c(-9.25,9),ylab="",type="l")
V=cumsum(rhoest^(2*(1:H)))*s
polygon(c(u,rev(u)),c(P+1.96*sqrt(V),
rev(P-1.96*sqrt(V))),col="yellow",border=NA)
polygon(c(u,rev(u)),c(P+1.64*sqrt(V),
rev(P-1.64*sqrt(V))),col="orange",border=NA)
lines(u,P,col="red")
Here, forecasts can be derived, with any kind of possible autoregressive coefficient, from 0.7 to 1. I.e. we can chose to model the time series either with a stationary, or an integrated series,
.
As we can see above, assuming either that the series is stationary (parameter lower – strictly – than 1) or integrated (parameter equal to 1), the shape of the prediction can be quite different. So yes, assuming an integrated model is a big deal, since it has a strong impact on predictions.

To leave a comment for the author, please follow the link and comment on their blog: Freakonometrics - Tag - R-english.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

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)