Estimating Ornstein-Uhlenbeck process drift

Question

What is the easiest way to obtain a drift parameter of O-U process given I have $\mu$?

Is it ok to linearize the O-U process like so:

$P_{t} = \mu + \phi(P_{t-1}-\mu)+\xi_t$

Form vectors from historic data:

$$ A = \begin{bmatrix} \ P_0-\mu \\ \ P_1-\mu \\ \ \dots \\ \ P_T-1-\mu \\ \end{bmatrix} $$

$$ b = \begin{bmatrix} \ \mu \\ \ \mu \\ \ \dots \\ \ \dots \\ \end{bmatrix} $$

$$ Y = \begin{bmatrix} \ P_1 \\ \ P_2 \\ \ \dots \\ \ P_T \\ \end{bmatrix} $$

And solve $\phi$ with OLS?

Cheers!

Answer 1

yes, using a rolling AR-1 and μ