ForecastHMMPdf {GaussianHMM1d}

Density function of a Gaussian HMM at time n+k

Description

This function computes the density function of a Gaussian HMM at time n+k, given observation up to time n.

Usage

ForecastHMMPdf(x, mu, sigma, Q, eta, k)

Arguments

x

points at which the density function is comptuted (mx1);

mu

vector of means for each regime (r x 1);

sigma

vector of standard deviations for each regime (r x 1);

Q

transition probality matrix (r x r);

eta

vector of the estimated probability of each regime (r x 1) at time n;

k

time of prediction.

Value

f

values of the density function at time n+k

w

weights of the mixture

Author(s)

Bouchra R Nasri and Bruno N Rémillard, January 31, 2019

References

Chapter 10.2 of B. Rémillard (2013). Statistical Methods for Financial Engineering, Chapman and Hall/CRC Financial Mathematics Series, Taylor & Francis.

Examples

mu <- c(-0.3 ,0.7) ; sigma <- c(0.15,0.05); Q <- matrix(c(0.8, 0.3, 0.2, 0.7),2,2) ;
eta <- c(.9,.1);
x <- seq(-1, 1, by = 0.01)
out <- ForecastHMMPdf(x,mu,sigma,Q,eta,3)
plot(x,out$f,type="l")