ParamMHMMR-class: A Reference Class which contains parameters of a MHMMR model.

Description

ParamMHMMR contains all the parameters of a MHMMR model. The parameters are calculated by the initialization Method and then updated by the Method implementing the M-Step of the EM algorithm.

Arguments

Fields

mData: MData object representing the sample (covariates/inputs X and observed multivariate responses/outputs Y).

K

The number of regimes (MHMMR components).

p

The order of the polynomial regression.

variance_type

Character indicating if the model is homoskedastic (variance_type = "homoskedastic") or heteroskedastic (variance_type = "heteroskedastic"). By default the model is heteroskedastic.

prior

The prior probabilities of the Markov chain. prior is a row matrix of dimension \((1, K)\).

trans_mat

The transition matrix of the Markov chain. trans_mat is a matrix of dimension \((K, K)\).

mask

Mask applied to the transition matrices trans_mat. By default, a mask of order one is applied.

beta

Parameters of the polynomial regressions. \(\boldsymbol{\beta} = (\boldsymbol{\beta}_{1},\dots,\boldsymbol{\beta}_{K})\) is an array of dimension \((p + 1, d, K)\), with p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K regimes. If MRHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is an array of size \((d, d, K)\) (otherwise MRHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size \((d, d)\)).

nu

The degree of freedom of the MHMMR model representing the complexity of the model.

phi

A list giving the regression design matrices for the polynomial and the logistic regressions.

Methods

initParam(try_algo = 1)

Method to initialize parameters prior, trans_mat, beta and sigma2.

If try_algo = 1 then beta and sigma2 are initialized by segmenting the time series Y uniformly into K contiguous segments. Otherwise, beta and sigma2 are initialized by segmenting randomly the time series Y into K segments.

MStep(statMHMMR)

Method which implements the M-step of the EM algorithm to learn the parameters of the MHMMR model based on statistics provided by the object statMHMMR of class StatMHMMR (which contains the E-step).