GofHMMGen: Goodness-of-fit of univariate hidden Markov model

In GenHMM1d: Goodness-of-Fit for Zero-Inflated Univariate Hidden Markov Models

Goodness-of-fit of univariate hidden Markov model

Description

This function performs a goodness-of-fit test for a univariate hidden Markov model

Usage

GofHMMGen(
  y,
  ZI = 0,
  reg,
  family,
  start = 0,
  max_iter = 10000,
  eps = 1e-04,
  size = 0,
  n_samples = 1000,
  n_cores = 1
)

Arguments

y	observations
ZI	1 if zero-inflated, 0 otherwise (default)
reg	number of regimes
family	distribution name; run the function distributions() for help
start	starting parameter for the estimation
max_iter	maximum number of iterations of the EM algorithm; suggestion 10000
eps	precision (stopping criteria); suggestion 0.0001.
size	additional parameter for some discrete distributions; run the command distributions() for help
n_samples	number of bootstrap samples; suggestion 1000
n_cores	number of cores to use in the parallel computing

Value

pvalue	pvalue of the Cramer-von Mises statistic in percent
theta	Estimated parameters; (r x p)
Q	estimated transition matrix; ; (r x r)
eta	(conditional probabilities of being in regime k at time t given observations up to time t; (n x r)
lambda	conditional probabilities of being in regime k at time t given all observations; (n x r)
U	pseudo-observations that should be uniformly distributed under the null hypothesis
cvm	Cramer-von-Mises statistic for goodness-of-fit
W	matrix of Rosenblatt transforms; (n x r)
LL	log-likelihood
nu	stationary distribution
AIC	Akaike information criterion
BIC	bayesian information criterion
CAIC	consistent Akaike information criterion
AICcorrected	Akaike information criterion corrected
HQC	Hannan-Quinn information criterion
stats	Empirical means and standard deviation of each regimes using lambda
pred_l	Estimated regime using lambda
pred_e	Estimated regime using eta
runs_l	Estimated number of runs using lambda
runs_e	Estimated number of runs using eta

Examples

family = "gaussian"
Q = matrix(c(0.8, 0.3, 0.2, 0.7), 2, 2) ; theta = matrix(c(0, 1.7, 0, 1),2,2) ;
y = SimHMMGen(theta, size=0, Q, ZI=1, family,  100)$SimData
out=GofHMMGen(y,1,2,family,n_samples=10)

GenHMM1d documentation built on Sept. 9, 2025, 5:50 p.m.