mixARemFixedPoint {mixAR}

EM estimation for mixture autoregressive models

Description

Fit a mixture autoregressive model to a univariate time series using the EM algorithm.

Usage

mixARemFixedPoint(y, model, est_shift = TRUE, crit = 1e-14, 
                  maxniter = 200, minniter = 10, verbose = FALSE)

mixARgenemFixedPoint(y, model, crit = 1e-14, maxniter = 200, 
                     minniter = 10, verbose = FALSE, ...)

Arguments

y

a univariate time series.

model

an object of class MixAR, a mixture autoregressive model providing the model specifications and initial values for the parameters.

est_shift

if TRUE optimise also w.r.t. the shift (constant) terms of the AR components, if FALSE keep the shift terms fixed.

crit

stop iterations when the relative change in the log-likelihood becomes smaller than this value.

maxniter

maximum number of iterations.

minniter

minimum number of iterations, do at leat that many iterations.

...

further arguments to be passed on to the M-step optimiser.

verbose

print more details during optimisation.

Details

mixARemFixedPoint and mixARgenemFixedPoint estimate MixAR models with the EM algorithm. For mixARemFixedPoint, the distribution of the components are fixed to be Gaussian. For mixARgenemFixedPoint, the distributions can, in principle be arbitrary (well, to a point).

Starting with model, the expectation and maximisation steps of the EM algorithm are repeated until convergence is detected or the maximum number of iterations, maxniter is exceeded.

Currently the convergence check is very basic—the iterations stop when the relative change in the log-likelihood in the last two iterations is smaller than the threshold value specified by crit and at least minniter iterations have been done.

The EM algorithm may converge very slowly. To do additional iterations use the returned value in another call of this function.

Value

the fitted model as an object inheriting from "MixAR".

Note

This function was not intended to be called directly by the user (hence the inconvenient name).

Author(s)

Georgi N. Boshnakov

See Also

fit_mixAR which uses these functions for estimation, classes "MixARGaussian", "MixARgen"

Examples

## data(ibmclose, package = "fma") # ibm data from BJ

m0 <- exampleModels$WL_ibm
m1 <- mixARemFixedPoint(fma::ibmclose, m0)
m1a <- mixARemFixedPoint(fma::ibmclose, m1$model)
show_diff(m1$model, m1a$model)

mixARemFixedPoint(fma::ibmclose, m0, est_shift = FALSE)


## simulate a continuation of ibmclose, assuming m0
ts1 <- mixAR_sim(m0, n = 50, init = c(346, 352, 357), nskip = 0)
m2a <- mixARemFixedPoint(ts1,       m0, est_shift = FALSE)$model
m2b <- mixARemFixedPoint(diff(ts1), m0, est_shift = FALSE)$model