predict-est.Merton-method: Prediction for a jump diffusion process

In SimoneHermann/BaPreStoPro: Bayesian Prediction of Stochastic Processes

Description

Bayesian prediction of a stochastic process Y_t = y_0 \exp( φ t - γ2/2 t+γ W_t + \log(1+θ) N_t).

Usage

## S4 method for signature 'est.Merton'
predict(object, t, burnIn, thinning, Lambda.mat,
  which.series = c("new", "current"), M2pred = 10, only.interval = TRUE,
  level = 0.05, cand.length = 1000, pred.alg = c("Distribution",
  "Trajectory", "simpleTrajectory", "simpleBayesTrajectory"), sample.length,
  plot.prediction = TRUE)

Arguments

object	class object of MCMC samples: "est.Merton", created with method estimate,Merton-method
t	vector of time points to make predictions for
burnIn	burn-in period
thinning	thinning rate
Lambda.mat	matrix-wise definition of intensity rate function (makes it faster)
which.series	which series to be predicted, new one ("new") or further development of current one ("current")
M2pred	optional, if current series to be predicted and t missing, M2pred variables will be predicted with the observation time distances
only.interval	if TRUE: only calculation of prediction intervals (only for pred.alg = "Distribution")
level	level of the prediction intervals
cand.length	length of candidate samples (if method = "vector"), for jump diffusion
pred.alg	prediction algorithm, "Distribution", "Trajectory", "simpleTrajectory" or "simpleBayesTrajectory"
sample.length	number of samples to be drawn, default is the number of posterior samples
plot.prediction	if TRUE, prediction intervals are plotted

References

Hermann, S. (2016a). BaPreStoPro: an R Package for Bayesian Prediction of Stochastic Processes. SFB 823 discussion paper 28/16.

Hermann, S. (2016b). Bayesian Prediction for Stochastic Processes based on the Euler Approximation Scheme. SFB 823 discussion paper 27/16.

Examples

cl <- set.to.class("Merton",
               parameter = list(thetaT = 0.1, phi = 0.05, gamma2 = 0.1, xi = c(3, 1/4)),
               Lambda = function(t, xi) (t/xi[2])^xi[1])
t <- seq(0, 1, by = 0.01)
data <- simulate(cl, t = t, y0 = 0.5)
est <- estimate(cl, t, data, 1000)
plot(est)
## Not run: 
pred1 <- predict(est, Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1])
pred2 <- predict(est, Lambda.mat = function(t, xi) (t/xi[,2])^xi[,1], pred.alg = "Trajectory")
pred3 <- predict(est, pred.alg = "simpleTrajectory")
pred4 <- predict(est, pred.alg = "simpleBayesTrajectory")

## End(Not run)

SimoneHermann/BaPreStoPro documentation built on May 9, 2019, 1:46 p.m.