LS.whittle.loglik: Locally Stationary Whittle log-likelihood Function

In pachamaltese/lsts: Locally Stationary Time Series

Locally Stationary Whittle log-likelihood Function

Description

This function computes Whittle estimator for LS-ARMA and LS-ARFIMA models, in data with mean zero. If mean is not zero, then it is subtracted to data.

Usage

LS.whittle.loglik(
  x,
  series,
  order = c(p = 0, q = 0),
  ar.order = NULL,
  ma.order = NULL,
  sd.order = NULL,
  d.order = NULL,
  include.d = FALSE,
  N = NULL,
  S = NULL,
  include.taper = TRUE
)

Arguments

x	(type: numeric) parameter vector.
series	(type: numeric) univariate time series.
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.
N	(type: numeric) value corresponding to the length of the window to compute periodogram. If N=NULL then the function will use N = \textrm{trunc}(n^{0.8}), see Dahlhaus (1998) where n is the length of the y vector.
S	(type: numeric) value corresponding to the lag with which will go taking the blocks or windows.
include.taper	(type: logical) logical argument that by default is TRUE. See periodogram.

Details

The estimation of the time-varying parameters can be carried out by means of the Whittle log-likelihood function proposed by Dahlhaus (1997),

L_n(\theta) = \frac{1}{4\pi}\frac{1}{M} \int_{-\pi}^{\pi} \bigg\{log f_{\theta}(u_j,\lambda) + \frac{I_N(u_j, \lambda)}{f_{\theta}(u_j,\lambda)}\bigg\}\,d\lambda

where M is the number of blocks, N the length of the series per block, n =S(M-1)+N, S is the shift from block to block, u_j =t_j/n, t_j =S(j-1)+N/2, j =1,\ldots,M and \lambda the Fourier frequencies in the block (2\,\pi\,k/N, k = 1,\ldots, N).

References

For more information on theoretical foundations and estimation methods see \insertRefbrockwell2002introductionLSTS \insertRefpalma2010efficientLSTS

See Also

nlminb, LS.kalman

pachamaltese/lsts documentation built on Jan. 27, 2024, 4:39 a.m.