BaPreStoPro (version 0.1)

estimate,Merton-method: Estimation for jump diffusion process

Description

Bayesian estimation of a stochastic process $Y_t = y_0 \exp( \phi t - \gamma^2/2 t+\gamma W_t + \log(1+\theta) N_t)$.

Usage

"estimate"(model.class, t, data, nMCMC, propSd, adapt = TRUE, proposal = c("normal", "lognormal"), it.xi = 10)

Arguments

model.class

class of the jump diffusion model including all required information, see Merton-class

t

vector of time points

data

vector of observation variables

nMCMC

length of Markov chain

propSd

vector of proposal variances for $\xi$

adapt

if TRUE (default), proposal variance is adapted

proposal

proposal density for xi: "normal" (default) or "lognormal"

it.xi

number of iterations for MH step for $\xi$ inside the Gibbs sampler

References

Hermann, S. and F. Ruggeri (2016). Modelling Wear Degradation in Cylinder Liners. SFB 823 discussion paper 06/16.

Hermann, S., K. Ickstadt and C. H. Mueller (2015). Bayesian Prediction for a Jump Diffusion Process with Application to Crack Growth in Fatigue Experiments. SFB 823 discussion paper 30/15.

Examples

model <- set.to.class("Merton", parameter = list(thetaT = 0.1, phi = 0.05, gamma2 = 0.1, xi = 10))
t <- seq(0, 1, by = 0.01)
data <- simulate(model, t = t, y0 = 0.5, plot.series = TRUE)
est <- estimate(model, t, data, 1000)
plot(est)
## Not run: 
# est_hidden <- estimate(model, t, data$Y, 1000)
# plot(est_hidden)
# ## End(Not run)