Estimate parameters of an Ornstein-Uhlenbeck process.

Source: R/ou_fit.R

Calculate the MLE using least-squares on the one-step Euler approximation.

ou_fit(Xt, dt)

Arguments

Xt

Vector of log-prices.

dt

Interobservation time.

Value

A named vector containing the maximum likelihood estimate of the OU parameters.

Details

The Ornstein-Uhlenbeck process is described by the stochastic differential equation

dXt = - gamma (Xt - mu) dt + sigma dBt.

Here, the MLE is computed analytically from the Euler approximation

X_{t+1} | X_t ~ N(X_t - gamma (X_t - mu) dt, sigma^2 dt).