init.theta.MSAR.VM: Initialisation function for von Mises MSAR model fitting

In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

Description

Initialization before fitting von Mises (non) homogeneous Markov switching autoregressive models by EM algorithm. Non homogeneity may be introduce in the probability transitions. The link function is defined here.

Usage

init.theta.MSAR.VM(data, ..., M, order, 
                  regime_names = NULL, 
                  nh.emissions = NULL, nh.transitions = NULL, 
                  label = NULL, ncov.emis = 0, ncov.trans = 0)

Arguments

data	array of univariate or multivariate series with dimension T*N.samples*d with T: number of time steps of each sample, N.samples: number of realisations of the same stationary process, d: dimension
M	number of regimes
order	order of AR processes
label	"HH" (default) for homogeneous MS AR model "NH" for non homogeneous transitions
regime_names	(optional) regime's names may be chosen
nh.emissions	not available - under development.
nh.transitions	link function for non homogeneous transitions. Default: von Mises (see details).
ncov.emis	not available - under development.
ncov.trans	number of covariates in NH model
...

Details

The model with non homogeneous transitions is labeled "NH" and it is written

P(X_t|X_{t-1}=x_{t-1}) = q(z_t,θ_{z_t})

with X_t the hidden process and q von Mises link function such that

p_1(x_t|x_{t-1},z_{t}) =\frac{ q_{x_{t-1},x_t}≤ft|\exp ≤ft(\tildeλ_{x_{t-1},x_t} e^{-iz_{t}} \right)\right|} {∑_{x'=1}^M q_{x_{t-1},x'}≤ft|\exp ≤ft(\tildeλ_{x_{t-1},x'} e^{-iz_{t}} \right)\right|},

with \tildeλ_{x,x'} a complex parameter (by taking \tildeλ_{x,x'}=λ_{x,x'} e^{iψ_{x,x'}}).

Value

return a list of class MSAR including

theta	parameter
..$transmat	transition matrix
..$prior	prior probabilities
..$mu	vector of intercepts
..$kappa	matrix of 'AR' coefficients (not complex by default)
..$par.emis	parameters of non homogeneous emissions (not used)
..$par.trans	parameters of non homogeneous transitions
label	model's label

Author(s)

Val\'erie Monbet, [e-mail]

References

Ailliot P., Bessac J., Monbet V., Pene F., (2014) Non-homogeneous hidden Markov-switching models for wind time series. JSPI.

See Also

fit.MSAR.VM

NHMSAR documentation built on Feb. 9, 2022, 9:06 a.m.