Fit time series regression models with mixture autoregressive residuals

Estimate a linear regression model for time series with residuals from a mixture autoregressive process.

Usage

fit_mixARreg(x, y, mixARmodel, EMinit, ...)

mixARreg(x, y, mixARmodel, tol = 1e-6, niter = 200)

Arguments

x

the response time series (currently a numeric vector).

y

data.frame, matrix or numeric vector. If either of the first two, each column must contain one covariate (currently numeric). A check for matching lengths between x and y is done.

mixARmodel

An object inheriting from class "MixAR", giving initial values for EM-estimation of mixture autoregressive parameters. Currenlty only "MixARGaussian" is supported.

EMinit

starting values for EM estimation of MixAR parameters. If present, must be a named list, containing at least prob and scale as numeric vectors, and a list for arcoef.

tol

threshold for convergence criterion.

...

passed on to MixARreg.

niter

maximal number of iterations.

Details

fit_mixARreg is a generic function. Currently there is no default method for fit_mixARreg. Arguments y, mixARmodel, EMinit can be given in a number of ways, see individual methods for details.

Argument mixARmodel gives the details of the the MixAR part of the model and initial values for the parameters. For fit_mixARreg this can alternatively be done with a list using argument EMinit. Currently, at least one of the two must be supplied, and if both are present EMinit is ignored.

mixARreg performs a two-step estimation of a linear regression model with mixture autoregressive residuals. It is the workhorse for fit_mixARreg which calls it to do the computations.

Value

reg

The summary output of the regression part of the model.

mixARmodel

Estimates of the mixture autoregressive part of the model.

niter

The number of iterations until convergence.

Methods

signature(x = "ANY", y = "data.frame", mixARmodel = "MixAR", EMinit = "missing")

Covariates y are supplied as data.frame: each column corresponds to one covariate. Initialization of MixAR paramters is done using input mixARmodel

signature(x = "ANY", y = "matrix", mixARmodel = "MixAR", EMinit = "missing")

Covariates y are supplied as matrix: each column corresponds to one covariate. Initialization of MixAR paramters is done using input mixARmodel

signature(x = "ANY", y = "numeric", mixARmodel = "MixAR", EMinit = "missing")

Covariates y is supplied as numeric: this method handles the simple regression case with a single covairate. Initialization of MixAR paramters is done using input mixARmodel

%\item{\code{signature(x = "ANY", y = "ANY", mixARmodel = "ANY", EMinit = "ANY")}}{}

signature(x = "ANY", y = "ANY", mixARmodel = "missing", EMinit = "list")

EMinit must be a named list (see 'Arguments').

signature(x = "ANY", y = "ANY", mixARmodel = "MixAR", EMinit = "list")

When both mixARmodel and EMinit are supplied, the second is ignored.

Author

Davide Ravagli and Georgi N. Boshnakov

Note

Estimation is done using the function mixARreg within each method.

See also

fit_mixAR

Examples

## Simulate covariates
set.seed(1234)
n <- 50 # for CRAN
y <- data.frame(rnorm(n, 7, 1), rt(n, 3), rnorm(n, 3, 2))

## Build mixAR part
model <- new("MixARGaussian", 
             prob   = exampleModels$WL_At@prob,      # c(0.5, 0.5)
             scale  = exampleModels$WL_At@scale,     # c(1, 2)        
             arcoef = exampleModels$WL_At@arcoef@a ) # list(-0.5, 1.1)

## Simulate from MixAR part
u <- mixAR_sim(model, n, 0)

x <- 10 + y[, 1] + 3 * y[, 2] + 2 * y[, 3] + u

## Fit model

## Using MixARGaussian
fit_mixARreg(x = x, y = y, mixARmodel = model, niter = 3)
#> $reg
#> 
#> Call:
#> lm(formula = data.frame(xstar, y))
#> 
#> Coefficients:
#>    (Intercept)  rnorm.n..7..1.        rt.n..3.  rnorm.n..3..2.  
#>          7.325           1.558           2.831           1.805  
#> 
#> 
#> $mixARmodel
#> An object of class "MixARGaussian"
#> Number of components: 2 
#>        prob      shift scale    order ar_1     
#> Comp_1 0.5566597   0   1.057166   1   -0.475807
#> Comp_2 0.4433403   0   1.906334   1    1.005682
#> 
#> Distributions of the error components:
#> 	standard Gaussian
#> 
#> 
#> $niter
#> [1] 3
#> 
#> $convergence
#> [1] 1
#> 

## Using EMinit
EMinit <- list(prob = exampleModels$WL_At@prob, scale = exampleModels$WL_At@scale,
               arcoef = exampleModels$WL_At@arcoef@a)
fit_mixARreg(x = x, y = y, EMinit = EMinit, niter = 3)
#> $reg
#> 
#> Call:
#> lm(formula = data.frame(xstar, y))
#> 
#> Coefficients:
#>    (Intercept)  rnorm.n..7..1.        rt.n..3.  rnorm.n..3..2.  
#>          7.325           1.558           2.831           1.805  
#> 
#> 
#> $mixARmodel
#> An object of class "MixARGaussian"
#> Number of components: 2 
#>        prob      shift scale    order ar_1     
#> Comp_1 0.5566597   0   1.057166   1   -0.475807
#> Comp_2 0.4433403   0   1.906334   1    1.005682
#> 
#> Distributions of the error components:
#> 	standard Gaussian
#> 
#> 
#> $niter
#> [1] 3
#> 
#> $convergence
#> [1] 1
#>