ForecastHMMeta {GaussianHMM1d}

Estimated probabilities of the regimes given new observations

Description

This function computes the estimated probabilities of the regimes for a Gaussian HMM given new observation after time n. it also computes the associated weight of the Gaussian mixtures that can be used for forecasted density, cdf, or quantile function.

Usage

ForecastHMMeta(ynew, mu, sigma, Q, eta)

Arguments

ynew

new observations (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;

Value

etanew

values of the estimated probabilities at times n+1 to n+m, using the new observations

w

weights of the mixtures for periods n+1 to n+m

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(.1,.9);
x <- c(0.2,-0.1,0.73)
out <- ForecastHMMeta(x,mu,sigma,Q,eta)