R: An easy ar()-question

[hamudenben]

Hi All,
I'm trying to calibrate parametres for an Ornstein-Uhlenbeck model:
dx = h (m - x) dt + s dz,
where
h = speed of reversion
m = long-term equilibrium level
s = volatility

So, I created the following timeseries (data from Yahoo!Finance):

LoL.ts <- ts(LoL, start=c(2012,1), frequency=4)

And then I fitted a ar(1)-model

fit.LoL.ts <- ar(LoL.ts, order=1)

Which yielded the following:

> fit.LoL.ts
Call:
ar(x = LoL.ts, order.max = 1)

Coefficients:
1
0.959

Order selected 1 sigma^2 estimated as 0.1269

And

> fit.LoL.ts$x.mean
V1
3.751205

The way I interpret these results is that:

h = 0.959
m = 3.751205
s^2 = 0.1269

And that would give me the following Ornstein-Uhlenbeck process:

dx = 0.959 * (3.7512 - x) dt + 0.3562dz

Is that correct?

Thanks

 

[sjain]

You need to fit the solution of your 1-lag regression model to the solution of OU SDE (wiki), then match the moments.