# [R] fitting Ornstein-Uhlenbeck process by MAXIMUM LIKELYHOOD

cesare orsini castjam at hotmail.it
Sat Jul 21 00:04:30 CEST 2012

```Dear friends

i am trying to fit an Ornstein-Uhlenbeck process by MAXIMUM LIKELYHOOD
method.

i found these formulas on
http://www.sitmo.com/article/calibrating-the-ornstein-uhlenbeck-model/
this is the mean-reverting process

http://r.789695.n4.nabble.com/file/n4637271/process.txt process.txt

and this is the script that i am using.......

delta=n/n
Sxx=(Sx)^2
Syy=(Sy)^2
Sxy=Sx*Sy
mu = (Sy*Sxx - Sx*Sxy) / ( n*(Sxx - Sxy) - (Sx^2 - Sx*Sy) )
lambda = -log( (Sxy - mu*Sx - mu*Sy + n*mu^2) / (Sxx -2*mu*Sx + n*mu^2)
)/delta
a = exp(-lambda*delta)
sigmah2 = (Syy - 2*a*Sxy + a^2*Sxx - 2*mu*(1-a)*(Sy - a*Sx) +
n*mu^2*(1-a)^2)/n;
sigma = sqrt((sigmah2)*2*lambda/(1-a^2))
theta=list(lambda=lambda, mu=mu,sigma=sigma,sigmah2=sigmah2)
return(theta)
}

where is my error?
is there some other script to obtain a good result by the same method?

thank you!!! :-)

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