GofHMM1d: Goodness-of-fit test of a univariate Gaussian Hidden Markov...

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

Goodness-of-fit test of a univariate Gaussian Hidden Markov Model

Description

This function performs a goodness-of-fit test of a Gaussian HMM based on a Cramér-von Mises statistic using parametric bootstrap.

Usage

GofHMM1d(y, reg, max_iter = 10000, eps = 1e-04, n_sample = 1000, n_cores)

Arguments

y	(n x 1) data vector
reg	number of regimes
max_iter	maxmimum number of iterations of the EM algorithm; suggestion 10 000
eps	eps (stopping criteria); suggestion 0.0001
n_sample	number of bootstrap samples; suggestion 1000
n_cores	number of cores to use in the parallel computing

Value

pvalue	pvalue of the Cram\'er-von Mises statistic in percent
mu	estimated mean for each regime
sigma	estimated standard deviation for each regime
Q	(reg x reg) estimated transition matrix
eta	(n x reg) conditional 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
W	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
gof <- GofHMM1d(data, 2, max_iter=10000, eps=0.0001, n_sample=100,n_cores=2)

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