GaussianHMM1d (version 1.1.2)

EstHMM1d: Estimation of a univariate Gaussian Hidden Markov Model (HMM)

Description

This function estimates parameters (mu, sigma, Q) of a univariate Hidden Markov Model. It computes also the probability of being in each regime, given the past observations (eta) and the whole series (lambda). The conditional distribution given past observations is applied to obtains pseudo-observations W that should be uniformly distributed under the null hypothesis. A Cramér-von Mises test statistic is then computed.

Usage

EstHMM1d(y, reg, max_iter = 10000, eps = 1e-04)

Value

mu

estimated mean for each regime

sigma

stimated standard deviation for each regime

Q

(reg x reg) estimated transition matrix

eta

(n x reg) probabilities of being in regime k at time t given observations up to time t

lambda

(n x reg) probabilities of being in regime k at time t given all observations

cvm

Cramér-von Mises statistic for the goodness-of-fit test

U

Pseudo-observations that should be uniformly distributed under the null hypothesis of a Gaussian HMM

LL

Log-likelihood

Arguments

y

(nx1) vector of data

reg

number of regimes

max_iter

maximum number of iterations of the EM algorithm; suggestion 10 000

eps

precision (stopping criteria); suggestion 0.0001.

Author

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

Q <- matrix(c(0.8, 0.3, 0.2, 0.7),2,2); mu <- c(-0.3 ,0.7) ; sigma <- c(0.15,0.05)
data <- Sim.HMM.Gaussian.1d(mu,sigma,Q,eta0=1,100)$x
est <- EstHMM1d(data, 2, max_iter=10000, eps=0.0001)