R Notebook

Random walk with Drift

\(x_t\)=\(\delta\)+\(x_t-_1\) +\(\omega_t\) for t=1,2,3,….. with the condition \(x_0\) =0 and \(\omega_t\) is white noise. The constant \(\delta\) is called drift.

set.seed(12)
#White noise 
w=rnorm(100,0,1)
#Random walk without drift
x=cumsum(w)  #cummulative sum
#Random walk with drift 0.5
wd=w+0.5
xd=cumsum(wd)
plot.ts(xd,main="random Walk",col="red",ylim=c(-10,60))
lines(x)

lines(.5*(1:200), lty="dashed")