GaussianHMM1d (version 1.1.2)

GofHMM1d: 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)

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

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

Author

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

# \donttest{
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)
# }