mleOu {sdetorus}

Maximum likelihood estimation of the OU diffusion

Description

Computation of the maximum likelihood estimator of the parameters of the univariate Ornstein–Uhlenbeck (OU) diffusion from a discretized trajectory \{X_{\Delta i}\}_{i=1}^N. The objective function to minimize is

\sum_{i=2}^n\log p_{\Delta}(X_{\Delta i} | X_{\Delta (i - 1)}).

Usage

mleOu(data, delta, alpha = NA, mu = NA, sigma = NA, start,
  lower = c(0.01, -5, 0.01), upper = c(25, 5, 25), ...)

Arguments

data

a vector of size N with the discretized trajectory of the diffusion.

delta

time discretization step.

alpha, mu, sigma

arguments to fix a parameter to a given value and perform the estimation on the rest. Defaults to NA, meaning that the parameter is estimated. Note that start, lower and upper must be changed accordingly if parameters are fixed, see examples.

start

starting values, a matrix with p columns, with each entry representing a different starting value.

lower, upper

bound for box constraints as in method "L-BFGS-B" of optim.

...

further arguments to be passed to mleOptimWrapper.

Details

The first element in data is not taken into account for estimation. See mleMou for the multivariate case (less efficient for dimension one).

Value

Output from mleOptimWrapper.

Examples

set.seed(345678)
data <- rTrajOu(x0 = 0, alpha = 1, mu = 0, sigma = 1, N = 100, delta = 0.1)
mleOu(data = data, delta = 0.1, start = c(2, 1, 2), lower = c(0.1, -10, 0.1),
      upper = c(25, 10, 25))

# Fixed sigma and mu
mleOu(data = data, delta = 0.1, mu = 0, sigma = 1, start = 2, lower = 0.1,
      upper = 25, optMethod = "nlm")