[R] Time Series DGPs

Pfaff, Bernhard Bernhard.Pfaff at drkw.com
Thu Sep 25 16:10:38 CEST 2003

>   I was wondering if anyone had some sample time series dgp 
> code.  I am 
> particularly interested in examples of autoregressive processes and 
> error correction model DGPs.  I have attached a more specific example 
> of what I mean.  I have tried myself but would hoping someone 
> had some 
> more elegant code that would help me extend my own code.
Hello Luke,

your setting does not qualify exactly as an ECM (both series have to be of
the same integration order, i.e. I(1) *and* there exists a linear
combination between them, which is I(0) -- see for instance Engle/Grangers'
seminal paper).

However, you can set up a sample ECM by generating an I(1) series, construct
a linear combination to produce a second one, run a regression and save the
residuals and finally enter these lagged by one period into your ECM.
Incidentally, avoid inclusion of contemporaneous differenced Xs due to
simultaneity-bias. Something, as follows should work:

# function for producing lags
tslag <- function(x, d=1)
  n <- length(x)
# generate a RW
x1 <- rnorm(100)
x <- cumsum(x1)
# generate artifically another I(1)-variable that is linearly dependent
y <- 0.8*x + rnorm(100)
# run ci-regression and save error (lagged one period)
ci.lm <- summary(lm(y~x))
error <- tslag(ci.lm$residuals)
# estimate ECM
y.diff <- y - tslag(y)
x.diff.l1 <- tslag(x-tslag(x))
ecm.lm <- summary(lm(y.diff~x.diff.l1+error))


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