# [R] Random walk

Sergio Andrés Estay Cabrera sestay at bio.puc.cl
Mon May 10 20:55:09 CEST 2010

Dear R users and specially Albyn and Giovanni,

thanks for your answers, but in fact I supposed the same at the
beginning of my problem. However, when I generate the data seldom I
obtain the expected correlation. For example using this code:

fz<-function(n,t,rho){
f<-NULL
for(i in 1:n){
s<-rmvnorm(n=t,mean=c(0,0),sigma=matrix(c(1,rho,rho,1),ncol=2),method='svd')
paso<-cor(cumsum(s[,1]),cumsum(s[,2]))
f<-c(f,paso)}
f<-f
}

and then plot the histogram of the results, it is possible to observe
that the distribution of the values is asymmetric with most of the
simulations close to 1 when the value of rho is higher than 0.3 and
looks like a uniform distribution with values below 0.3.

I suspect than the only possibility is using a brute force algorithm.

Sergio A. Estay
*CASEB *
Departamento de Ecología

Albyn Jones wrote:
> Sums of correlated increments have the same correlation as the original
> variables...
>
>  library(mvtnorm)
>  X<- matrix(0,nrow=1000,ncol=2)
>  for(i in 1:1000){
>  Y <- rmvnorm(1000,mean=mu,sigma=S)
>  X[i,] <- apply(Y,2,sum)
>  }
>  cor(Y)
>           [,1]      [,2]
> [1,] 1.0000000 0.4909281
> [2,] 0.4909281 1.0000000
>
> So, unless you meant that you want the _sample_ correlation to be
> pre-specified, you are all set.
>
> albyn
>
> On Sun, May 09, 2010 at 09:20:25PM -0400, Sergio Andrés Estay Cabrera wrote:
>
>> Hi everybody,
>>
>>
>> I am trying to generate two random walks with an specific correlation, for
>> example, two random walks of 200 time steps with a correlation 0.7.
>>
>> I built the random walks with:
>>
>> x<-cumsum(rnorm(200, mean=0,sd=1))
>> y<-cumsum(rnorm(200, mean=0,sd=1))
>>
>> but I don't know how to fix the correlation between them.
>>
>> With white noise is easy to fix the correlation using the function rmvnorm
>> in the package mvtnorm
>>
>> I surfed in the web in the searchable mail archives in the R web site but
>> no references appears.
>>
>> If you have some advices to solve this problems I would be very thankful.
>>
>>
>> Sergio A. Estay
>> *CASEB *
>> Departamento de Ecología
>>
>> --
>> “La disciplina no tiene ningún mérito en circunstancias ideales. ” – Habor Mallow
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
>
>

--
“La disciplina no tiene ningún mérito en circunstancias ideales. ” – Habor Mallow