GofHMMGen: Goodness-of-fit of univariate hidden Markov model
In GenHMM1d: Goodness-of-Fit for Univariate Hidden Markov Models

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

GofHMMGen(
  y,
  reg,
  family,
  start = 0,
  max_iter = 10000,
  eps = 0.001,
  graph = 0,
  size = 0,
  n_sample = 100,
  n_cores = 1,
  useFest = 1
)

`y`	observations
`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.
`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
`n_sample`	number of bootstrap samples; suggestion 1000
`n_cores`	number of cores to use in the parallel computing
`useFest`	1 (default) to use the first estimated parameters as starting value for the bootstrap, 0 otherwise

`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`	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