LSTS (version 2.1)

LS.kalman: Kalman filter for locally stationary processes

Description

This function run the state-space equations for expansion infinite of moving average in processes LS-ARMA or LS-ARFIMA.

Usage

LS.kalman(
  series,
  start,
  order = c(p = 0, q = 0),
  ar.order = NULL,
  ma.order = NULL,
  sd.order = NULL,
  d.order = NULL,
  include.d = FALSE,
  m = NULL
)

Arguments

series

(type: numeric) univariate time series.

start

(type: numeric) numeric vector, initial values for parameters to run the model.

order

(type: numeric) vector corresponding to ARMA model entered.

ar.order

(type: numeric) AR polimonial order.

ma.order

(type: numeric) MA polimonial order.

sd.order

(type: numeric) polinomial order noise scale factor.

d.order

(type: numeric) d polinomial order, where d is the ARFIMA parameter.

include.d

(type: numeric) logical argument for ARFIMA models. If include.d=FALSE then the model is an ARMA process.

m

(type: numeric) truncation order of the MA infinity process. By default \(m = 0.25n^{0.8}\) where n the length of series.

Value

A list with:

residuals

standard residuals.

fitted_values

model fitted values.

delta

variance prediction error.

Details

The model fit is done using the Whittle likelihood, while the generation of innovations is through Kalman Filter. Details about ar.order, ma.order, sd.order and d.order can be viewed in LS.whittle.

References

For more information on theoretical foundations and estimation methods see brockwell2002introductionLSTS palma2007longLSTS palma2013estimationLSTS

Examples

# NOT RUN {
fit_kalman <- LS.kalman(malleco, start(malleco))
# }