[R] Random walk

[David Winsemius]

On May 10, 2010, at 2:55 PM, Sergio Andrés Estay Cabrera wrote:

> 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
> }

I believe you may want to search on the term "quantos model". If you  
have two independent Brownian processes W_1(t) and W_2(t) then W_3 =  
rho*W_1(t) +sqrt(1-rho^2)*W_2(t) will theoretically have correlation  
rho with W_1. Sampling will of course giving varying instantiation  
values.


-- 
David
citation: "Financial Calculus", Baxter M; Rennie A (1996)
>
> 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.
>
>
> Any advice would be helpful
>
> Sergio A. Estay
> *CASEB *
> Departamento de Ecología
> Universidad Catolica de Chile
>
>
>
>
> 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.
>>>
>>> Thanks in advance.
>>>
>>> Sergio A. Estay
>>> *CASEB *
>>> Departamento de Ecología
>>> Universidad Catolica de Chile
>>>
>>> -- 
>>> “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
>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>
>>
>>
>
>
> -- 
> “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
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT