R help - Jan 2013 - simulation

Dear R users,
suppose we have a random walk such as:

v_t+1 = v_t + e_t+1

where e_t is a normal IID noise pocess with mean = m and standard deviation = sd
and v_t is the fundamental value of a stock.

Now suppose I want a trading strategy to be:

x_t+1 = c(v_t – p_t)

where c is a costant.
I know, from the paper where this equations come from (Farmer and Joshi, The
price dynamics of common trading strategies, 2001) that the induced price
dynamics is:

r_t+1 = –a*r_t + a*e_t + theta_t+1

and

p_t+1 = p_t +r_t+1

where r_t = p_t – p_t-1 , e_t = v_t – v_t-1 and a = c/lambda (lambda is another
constant).

How can I simulate the equations I have just presented?
I have good confidence with R for statistical analysis, but not for simulation
therefore I apologize for my ignorance.
What I came up with is the following:

##general settings
c<-0.5
lambda<-0.3
a<-c/lambda
n<-500 

## Eq.12 (the v_t random walk)
V_init_cond<-0
Et<-ts(rnorm(n+100,mean=0,sd=1))
Vt<-Et*0
Vt[1]<-V_init_cond+Et[1]
for(i in 2:(n+100)) {
Vt[i]<-Vt[i-1]+Et[i]
}
Vt<-ts(Vt[(length(Vt)-n+1):length(Vt)])
plot(Vt)

## Eq.13 (the strategy)
Xt_init_cond<-0
Xt<-Xt_init_cond*0
Xt[2]<-c(Vt[1]-Pt[1])
for(i in 2:(n)){
Xt[i]<-c(Vt[i-1]-Pt[i-1])
}
Xt<-ts(Xt[(length(Xt)-n+1):length(Xt)])
plot(Xt)

## Eq. 14 (pice dynamics)
P_init_cond<-0
Pt<-Rt*0
Pt[1]<-P_init_cond+Rt[1]
for(i in 2:(n+100)) {
Pt[i]<-Pt[i-1]+Rt[i]
}
Pt<-ts(Pt[(length(Pt)-n+1):length(Pt)])
plot(Pt)
Rt_init_cond<-0
Rt<-Rt_init_cond*0
Rt[2]<- -a*Rt[1]+a*Et[1]+e[2]
for(i in 2:(n)){
Rt[i]<- -a*Rt[i-1]+a*Et[i-1]+e[i]
}
Rt<-ts(Rt[(length(Rt)-n+1):length(Rt)])
plot(Rt)

I don’t think the code above is correct, and I don’t even know if this is the
approach I have to take.
Any suggestion is warmly appreciated.

thanks,
Simone Gogna 
	[[alternative HTML version deleted]]

On 03-01-2013, at 17:40, Simone Gogna <singletonthebest at msn.com> wrote:
> Dear R users,
> suppose we have a random walk such as:
> 
> v_t+1 = v_t + e_t+1
> 
> where e_t is a normal IID noise pocess with mean = m and standard deviation
= sd and v_t is the fundamental value of a stock.
> 
> Now suppose I want a trading strategy to be:
> 
> x_t+1 = c(v_t ? p_t)
> 
> where c is a costant.
> I know, from the paper where this equations come from (Farmer and Joshi,
The price dynamics of common trading strategies, 2001) that the induced price
dynamics is:
> 
> r_t+1 = ?a*r_t + a*e_t + theta_t+1
> 
> and
> 
> p_t+1 = p_t +r_t+1
> 
> where r_t = p_t ? p_t-1 , e_t = v_t ? v_t-1 and a = c/lambda (lambda is
another constant).
> 
> How can I simulate the equations I have just presented?
> I have good confidence with R for statistical analysis, but not for
simulation therefore I apologize for my ignorance.
> What I came up with is the following:
> 
> ##general settings
> c<-0.5
> lambda<-0.3
> a<-c/lambda
> n<-500 
> 
> ## Eq.12 (the v_t random walk)
> V_init_cond<-0
> Et<-ts(rnorm(n+100,mean=0,sd=1))
> Vt<-Et*0
> Vt[1]<-V_init_cond+Et[1]
> for(i in 2:(n+100)) {
> Vt[i]<-Vt[i-1]+Et[i]
> }
> Vt<-ts(Vt[(length(Vt)-n+1):length(Vt)])
> plot(Vt)
> 
> ## Eq.13 (the strategy)
> Xt_init_cond<-0
> Xt<-Xt_init_cond*0
> Xt[2]<-c(Vt[1]-Pt[1])
> for(i in 2:(n)){
> Xt[i]<-c(Vt[i-1]-Pt[i-1])
> }
> Xt<-ts(Xt[(length(Xt)-n+1):length(Xt)])
> plot(Xt)
> 
> ## Eq. 14 (pice dynamics)
> P_init_cond<-0
> Pt<-Rt*0
> Pt[1]<-P_init_cond+Rt[1]
> for(i in 2:(n+100)) {
> Pt[i]<-Pt[i-1]+Rt[i]
> }
> Pt<-ts(Pt[(length(Pt)-n+1):length(Pt)])
> plot(Pt)
> Rt_init_cond<-0
> Rt<-Rt_init_cond*0
> Rt[2]<- -a*Rt[1]+a*Et[1]+e[2]
> for(i in 2:(n)){
> Rt[i]<- -a*Rt[i-1]+a*Et[i-1]+e[i]
> }
> Rt<-ts(Rt[(length(Rt)-n+1):length(Rt)])
> plot(Rt)
> 
> I don?t think the code above is correct, and I don?t even know if this is
the approach I have to take.
> Any suggestion is warmly appreciated.
> 
Do not use "c" as a user variable. It is an R provided function.
You have a formulae such as

Xt[2]<-c(Vt[1]-Pt[1])
for(i in 2:(n)){
Xt[i]<-c(Vt[i-1]-Pt[i-1])

c is not doing here what you want.
I assume you meant to multiply as in

Xt[2]<-c*(Vt[1]-Pt[1])
for(i in 2:(n)){
Xt[i]<-c*(Vt[i-1]-Pt[i-1])


So call this constant cpar or something similar.

Where has e been defined?

If you reorder your equations in such a way that all initial conditions are
computed first in the correct order
then you simulation loops could be condensed into a single loop such as

for(i in 2:(n+100)) {
    Vt[i] <- Vt[i-1]+Et[i]
    Rt[i] <- -a*Rt[i-1]+a*Et[i-1]+e[i]
    Pt[i] <- Pt[i-1]+Rt[i]
    Xt[i] <- cpar*(Vt[i-1]-Pt[i-1])
}  

If I am correct.

Berend

On 03-01-2013, at 17:40, Simone Gogna <singletonthebest at msn.com> wrote:
> Dear R users,
> suppose we have a random walk such as:
> 
> v_t+1 = v_t + e_t+1
> 
> where e_t is a normal IID noise pocess with mean = m and standard deviation
= sd and v_t is the fundamental value of a stock.
> 
> Now suppose I want a trading strategy to be:
> 
> x_t+1 = c(v_t ? p_t)
> 
> where c is a costant.
> I know, from the paper where this equations come from (Farmer and Joshi,
The price dynamics of common trading strategies, 2001) that the induced price
dynamics is:
> 
> r_t+1 = ?a*r_t + a*e_t + theta_t+1
> 
> and
> 
> p_t+1 = p_t +r_t+1
> 
> where r_t = p_t ? p_t-1 , e_t = v_t ? v_t-1 and a = c/lambda (lambda is
another constant).
> 
> How can I simulate the equations I have just presented?
> I have good confidence with R for statistical analysis, but not for
simulation therefore I apologize for my ignorance.
> What I came up with is the following:
> 
> ##general settings
> c<-0.5
> lambda<-0.3
> a<-c/lambda
> n<-500 
> 
> ## Eq.12 (the v_t random walk)
> V_init_cond<-0
> Et<-ts(rnorm(n+100,mean=0,sd=1))
> Vt<-Et*0
> Vt[1]<-V_init_cond+Et[1]
> for(i in 2:(n+100)) {
> Vt[i]<-Vt[i-1]+Et[i]
> }
> Vt<-ts(Vt[(length(Vt)-n+1):length(Vt)])
> plot(Vt)
> 
> ## Eq.13 (the strategy)
> Xt_init_cond<-0
> Xt<-Xt_init_cond*0
> Xt[2]<-c(Vt[1]-Pt[1])
> for(i in 2:(n)){
> Xt[i]<-c(Vt[i-1]-Pt[i-1])
> }
> Xt<-ts(Xt[(length(Xt)-n+1):length(Xt)])
> plot(Xt)
> 
> ## Eq. 14 (pice dynamics)
> P_init_cond<-0
> Pt<-Rt*0
> Pt[1]<-P_init_cond+Rt[1]
> for(i in 2:(n+100)) {
> Pt[i]<-Pt[i-1]+Rt[i]
> }
> Pt<-ts(Pt[(length(Pt)-n+1):length(Pt)])
> plot(Pt)
> Rt_init_cond<-0
> Rt<-Rt_init_cond*0
> Rt[2]<- -a*Rt[1]+a*Et[1]+e[2]
> for(i in 2:(n)){
> Rt[i]<- -a*Rt[i-1]+a*Et[i-1]+e[i]
> }
> Rt<-ts(Rt[(length(Rt)-n+1):length(Rt)])
> plot(Rt)
> 
> I don?t think the code above is correct, and I don?t even know if this is
the approach I have to take.
> Any suggestion is warmly appreciated.

You should also have a look at package simecol which can also do discrete time
models.
It would certainly require some study of the manual and a bit of work on your
part but I think  it would be worth it.


Berend