samurais (version 0.1.0)

ParamHMMR-class: A Reference Class which contains parameters of a HMMR model.

Description

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

Fields

X

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

Y

Numeric vector of length m representing the observed response/output \(y_{1},\dots,y_{m}\).

m

Numeric. Length of the response/output vector Y.

K

The number of regimes (HMMR 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 a matrix of dimension \((p + 1, K)\), with p the order of the polynomial regression. p is fixed to 3 by default.

sigma2

The variances for the K regimes. If HMMR model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size \((K, 1)\) (otherwise HMMR model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size \((1, 1)\)).

nu

The degree of freedom of the HMMR 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 mask, 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(statHMMR)

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