Kalman filter for locally stationary processes

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

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 Brockwell PJ, Davis RA, Calder MV (2002). Introduction to time series and forecasting, volume 2. Springer. Palma W (2007). Long-memory time series: theory and methods, volume 662. John Wiley \& Sons. Palma W, Olea R, Ferreira G (2013). “Estimation and forecasting of locally stationary processes.” Journal of Forecasting, 32(1), 86--96.

Examples

fit_kalman <- LS.kalman(malleco, start(malleco))