Internal functions for estimation of MixAR models with Gaussian components

Internal functions for EM estimation of MixAR models with Gaussian components: sums of products and crossproducts; M-step for MixAR estimation; estimation of autoregressive part of the model.

Usage

tauCorrelate(y, tau, order)
tau2arcoef(y, tau, order, est_shift = TRUE)
mixMstep(y, tau, order, index, est_shift = TRUE)

Arguments

y: time series.
tau: conditional probabilties for the observations to belong to each of the components, a MixComp object.
order: order of the MixAR model, numeric vector of length the number of mixture components.
index: indices of the observations to include in the likelihood calculations, typically (p+1):n, where p is max(order) and n=length(y).
est_shift: if TRUE include shifts (intercepts) in the AR components, otherwise set them to zero.

Details

mixMstep performs an M-step for estimation of MixAR models with Gaussian components.

tauCorrelate computes crossproducts needed for EM estimation of MixAR models with Gaussian components.

tau2arcoef computes the AR coefficients by solving Yule-Walker-type equations for each component.

Value

For mixMstep, a MixAR model, an object of class MixARGaussian. For tauCorrelate, a named list with the following components:

Stau

Stauy
Stauyy

For tau2arcoef, a list with two components:

shift: the shift (intercept) terms, a numeric vector
arcoef: the AR coefficients as a list, whose i-th component contains the coefficients for component i (as a numeric vector)