emMHMMR {samurais}

emMHMMR implemens the EM (Baum-Welch) algorithm to fit a MHMMR model.

Description

emMHMMR implements the maximum-likelihood parameter estimation of the MHMMR model by the Expectation-Maximization (EM) algorithm, known as Baum-Welch algorithm in the context of HMMs.

Usage

emMHMMR(X, Y, K, p = 3, variance_type = c("heteroskedastic",
  "homoskedastic"), n_tries = 1, max_iter = 1500, threshold = 1e-06,
  verbose = FALSE)

Arguments

X

Numeric vector of length m representing the covariates/inputs x_{1},\dots,x_{m}.

Y

Matrix of size (m, d) representing a d dimension time series observed at points 1,\dots,m.

K

The number of regimes (MHMMR components).

p

Optional. The order of the polynomial regression. By default, p is set at 3.

variance_type

Optional character indicating if the model is "homoskedastic" or "heteroskedastic". By default the model is "heteroskedastic".

n_tries

Optional. Number of runs of the EM algorithm. The solution providing the highest log-likelihood will be returned.

If n_tries > 1, then for the first run, parameters are initialized by uniformly segmenting the data into K segments, and for the next runs, parameters are initialized by randomly segmenting the data into K contiguous segments.

max_iter

Optional. The maximum number of iterations for the EM algorithm.

threshold

Optional. A numeric value specifying the threshold for the relative difference of log-likelihood between two steps of the EM as stopping criteria.

verbose

Optional. A logical value indicating whether or not values of the log-likelihood should be printed during EM iterations.

Details

emMHMMR function implements the EM algorithm. This function starts with an initialization of the parameters done by the method initParam of the class ParamMHMMR, then it alternates between the E-Step (method of the class StatMHMMR) and the M-Step (method of the class ParamMHMMR) until convergence (until the relative variation of log-likelihood between two steps of the EM algorithm is less than the threshold parameter).

Value

EM returns an object of class ModelMHMMR.

See Also

ModelMHMMR, ParamMHMMR, StatMHMMR

Examples

data(multivtoydataset)

mhmmr <- emMHMMR(multivtoydataset$x, multivtoydataset[,c("y1", "y2", "y3")],
                 K = 5, p = 1, verbose = TRUE)

mhmmr$summary()

mhmmr$plot()