SDE loglikelihood function.

Evaluates the loglikelihood function given SDE data and parameter values.

sde.loglik(model, x, dt, theta, ncores = 1)

Arguments

model	An sde.model object.
x	A matrix or 3-d array of data with dim(x)[1] observations and dim(x)[2] == ndims.
dt	A scalar or vector of length dim(x)[1]-1 of time intervals between observations.
theta	A vector or matrix of parameters with nparams columns.
ncores	If model is compiled with OpenMP, the number of cores to use for parallel processing. Otherwise, uses ncores = 1 and gives a warning.

Value

A vector of loglikelihood evaluations, of the same length as the third dimension of x and/or first dimension of theta. If input contains invalid data or parameters an error is thrown.

Examples

# load Heston's model
hmod <- sde.examples("hest")

# Simulate data
nreps <- 10
nobs <- 100
theta <- c(alpha = 0.1, gamma = 1, beta = 0.8, sigma = 0.6, rho = -0.8)
Theta <- apply(t(replicate(nreps, theta)), 2, jitter)
x0 <- c(X = log(1000), Z = 0.1)
X0 <- apply(t(replicate(nreps,x0)), 2, jitter)
dT <- 1/252
hsim <- sde.sim(model = hmod, x0 = X0, theta = Theta,
                dt = dT, dt.sim = dT/10, nobs = nobs, nreps = nreps)
#> Number of normal draws required: 10000
#> Running simulation...
#> Execution time: 0 seconds.
#> Bad Draws = 0

# single parameter, single data
sde.loglik(model = hmod, x = hsim$data[,,1], dt = dT, theta = theta)
#> [1] 687.1985
# multiple parameters, single data
sde.loglik(model = hmod, x = hsim$data[,,1], dt = dT, theta = Theta)
#>  [1] 687.3319 687.2974 687.0353 686.8871 687.1530 687.0873 686.9992 687.1027
#>  [9] 687.0164 686.9412
# multiple parameters, multiple data
sde.loglik(model = hmod, x = hsim$data, dt = dT, theta = Theta)
#>  [1] 687.3319 726.3819 675.0533 624.7651 683.5307 701.0654 688.2960 673.7033
#>  [9] 655.8494 680.2702