[R] How to simulate a variable Xt=Wit+0.5Wit-1 with

Millo Giovanni Giovanni_Millo at Generali.com
Tue Jan 25 15:30:21 CET 2011

Dear Carlos,

please refrain from posting the same question umpteen times. Please
consider that code is hard to read and people might not have the time to
run your simulation etc. etc..

As I told you privately in response to your message on 18/1, 

> Re: generating correlated effects, I tried this only once, but I 
> didn't get it right. Simulations using this are, e.g., Hansen (2007) 
> http://faculty.chicagobooth.edu/christian.hansen/research/panel_cov_t.
> pdf
> and Drukker (2003)
> http://ideas.repec.org/a/tsj/stataj/v3y2003i2p168-177.html
> I suggest you take inspiration from what they did.

so the references are here for the possible benefit (?) of the list too.
In the meantime I looked at your code and it looks more or less OK to
me. I would have generated the correlated effects simply as
x_i=something random + gamma*u_i, but your Choleski approach is much
better. Sorry but a thorough check is beyond my time availability now.

arima.sim() may be a good way to go, I can't tell. The simplest way is
just to use loops: generating (in pseudo-R)

> w <- runif(n, <parameters>)
> x[1] <- <random> 

and then 

> for(i in 2:n) x[i] <- 0.5*x[i-1]+w[i]

PS remember to generate a sufficiently long sequence of x's *before*
those in your sample, in order to make the initial conditions

Let me suggest Ch. 7.1 of Kleiber and Zeileis, "Applied Econometrics
with R" for a nice and organized approach to (econometric) simulations
in R.
Other than this, it's just basic R, trying it out and seeing if it

Best wishes,

----------- original message -------------------

Message: 18
Date: Mon, 24 Jan 2011 14:38:43 +0000
From: carpan at sapo.pt
To: r-help <r-help at r-project.org>
Subject: [R] How to simulate a variable Xt=Wit+0.5Wit-1 with
Message-ID: <20110124143843.10742vvdq8rvqcxf at mail.sapo.pt>
Content-Type: text/plain; charset=ISO-8859-15; DelSp="Yes";

Dear all

I simulate a panel data:

n <- 10
t <- 5
nt <- n*t
pData <- data.frame(id = rep(paste("JohnDoe", 1:n, sep = "."), each =  
t),time = rep(1981:1985, n))
rho <-0.99#simulate alphai corelated with the xi
alphai <- rnorm(n,mean=0,sd=1)#alphai simulation
x<- as.matrix(rnorm(nt,1))#xi simulation
akro <- kronecker(alphai ,matrix(1,t,1))#kronecker of alphai
cormat<-matrix(c(1,rho,rho,1),nrow=2,ncol=2)#correlation matrix
cormat.chold <- chol(cormat)#choleski transformation of correlation
akrox <- cbind(akro,x)
ax <- akrox%*%cormat.chold
ai <- as.matrix(ax[,1])
xcorr <- as.matrix(ax[,2:(1+ncol(x))])
pData<-plm.data(pData, index = c("id", "time"))

But now i need a variable Xt=Wit+0.5Wit-1 with Wit~U(0,2),  the code i  
Try to use is:

for (i in 1:n) {
             p <- i*t
             m <- (i-1)*t+1
        for (j in m:p){
             xt<-arima.sim(n=nt, list(ar=c(0.5)))               }
Is this the correct  way to simulate the AR(1), without the assumption  
Wit~U(0,2)? How i simulate the variable with the assumption  
Wit~U(0,2), and put it in my dataframe correctly?
Comments and tips are welcome,


Carlos Br?s
Statistics Portugal-INE

---------- end original message -------------

Giovanni Millo
Research Dept.,
Assicurazioni Generali SpA
Via Machiavelli 4, 
34132 Trieste (Italy)
tel. +39 040 671184 
fax  +39 040 671160 

Ai sensi del D.Lgs. 196/2003 si precisa che le informazi...{{dropped:13}}

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