sdetorus (version 0.1.10)

approxMleWnPairs: Approximate MLE of the WN diffusion in 2D from a sample of initial and final pairs of angles.

Description

Approximate Maximum Likelihood Estimation (MLE) for the Wrapped Normal (WN) diffusion, using the wrapped Ornstein--Uhlenbeck diffusion and assuming initial stationarity.

Usage

approxMleWnPairs(data, delta, start = c(0, 0, 1, 1, 0, 1, 1),
  alpha = rep(NA, 3), mu = rep(NA, 2), sigma = rep(NA, 2), rho = NA,
  lower = c(-pi, -pi, 0.01, 0.01, -25, 0.01, 0.01, -0.99), upper = c(pi,
  pi, 25, 25, 25, 25, 25, 0.99), maxK = 2, expTrc = 30, ...)

Value

Output from mleOptimWrapper.

Arguments

data

a matrix of dimension c(n, p).

delta

discretization step.

start

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

alpha

vector of length 3 parametrizing the A matrix as in alphaToA.

mu

a vector of length 2 giving the mean.

sigma

vector of length 2 containing the square root of the diagonal of \(\Sigma\), the diffusion matrix.

rho

correlation coefficient of \(\Sigma\).

lower, upper

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

maxK

maximum absolute value of the windings considered in the computation of the WN.

expTrc

truncation for exponential: exp(x) with x <= -expTrc is set to zero. Defaults to 30.

...

further parameters passed to mleOptimWrapper.

Examples

mu <- c(0, 0)
alpha <- c(1, 2, 0.5)
sigma <- c(1, 1)
rho <- 0.5
set.seed(4567345)
begin <- rStatWn2D(n = 200, mu = mu, alpha = alpha, sigma = sigma)
end <- t(apply(begin, 1, function(x) rTrajWn2D(x0 = x, alpha = alpha,
                                               mu = mu, sigma = sigma,
                                               rho = rho, N = 1,
                                               delta = 0.1)[2, ]))
data <- cbind(begin, end)
approxMleWnPairs(data = data, delta = 0.1,
                 start = c(2, pi/2, 2, 0.5, 0, 2, 1, 0.5))