ParamRHLP-class function

A Reference Class which contains parameters of a RHLP model.

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

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 (RHLP components).

• p: The order of the polynomial regression.

• q: The dimension of the logistic regression. For the purpose of segmentation, it must be set to 1.

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

• W: Parameters of the logistic process. $W = (w_{1},\dots,w_{K-1})$

   is a matrix of dimension $(q + 1, K - 1)$, with `q` the order of the logistic regression. `q` is fixed to 1 by default.
  

• beta: Parameters of the polynomial regressions. c("$\\beta =\n$", "$(\\beta_{1},\\dots,\\beta_{K})$") 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 RHLP model is heteroskedastic (variance_type = "heteroskedastic") then sigma2 is a matrix of size $(K, 1)$ (otherwise RHLP model is homoskedastic (variance_type = "homoskedastic") and sigma2 is a matrix of size $(1, 1)$).

• nu: The degree of freedom of the RHLP 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 W, 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, `W`, `beta` and `sigma2` are initialized by segmenting randomly the time series `Y` into `K` segments.
  

• MStep(statRHLP, verbose_IRLS): Method which implements the M-step of the EM algorithm to learn the parameters of the RHLP model based on statistics provided by the object statRHLP of class StatRHLP (which contains the E-step).