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

In GaussianHMM1d: Inference, Goodness-of-Fit and Forecast for Univariate Gaussian Hidden Markov Models

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)

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.

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

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

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)

GaussianHMM1d documentation built on July 9, 2023, 6:52 p.m.