EstHMMGen: Estimation of univariate hidden Markov model

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

Description

This function estimates the parameters from a univariate hidden Markov model

Usage

EstHMMGen(
  y,
  reg,
  family,
  start = 0,
  max_iter = 10000,
  eps = 0.001,
  graph = 0,
  size = 0,
  theta0 = 0
)

Arguments

y	observations; (n x 1)
reg	number of regimes
family	distribution name; run the function distributions() for help
start	starting parameters for the estimation; (1 x p)
max_iter	maximum number of iterations of the EM algorithm; suggestion 10000
eps	precision (stopping criteria); suggestion 0.001.
graph	1 for a graph, 0 otherwise (default); only for continuous distributions
size	additional parameter for some discrete distributions; run the command distributions() for help
theta0	initial parameters for each regimes; (r x p)

Details

#############################################################################

Value

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	matrix of Rosenblatt transforms; (n x r)
cvm	cramer-von-Mises statistic for goodness-of-fit
W	pseudo-observations that should be uniformly distributed under the null hypothesis
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(-1.5, 1.7, 1, 1),2,2) ;
sim = SimHMMGen(Q, family, theta, 10)$SimData ;
est = EstHMMGen(y=sim, reg=2, family=family)

GenHMM1d documentation built on Jan. 21, 2021, 9:07 a.m.