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Last data update: 2014.03.03

R: Locally Stationary Whittle log-likelihood Function

LS.whittle.loglik

R Documentation

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`	parameter vector.
`series`	univariate time series.
`order`	vector with the specification of the ARMA model: the two integer components (p, q) are the AR order and the MA order.
`ar.order, ma.order`	AR and MA polimonial order, respectively. See details below.
`sd.order`	polinomial order noise scale factor.
`d.order`	`d` polinomial order, where `d` is the `ARFIMA` parameter.
`include.d`	logical argument for `ARFIMA` models. If `include.d=FALSE` then the model is an ARMA process.
`N`	value corresponding to the length of the window to compute periodogram. If `N=NULL` then the function will use N = \textmd{trunc}(n^{0.8}), see Dahlhaus (1998) where n is the length of the `y` vector.
`S`	value corresponding to the lag with which will go taking the blocks or windows.
`include.taper`	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(θ) = frac{1}{4π}frac{1}{M} int_{-π}^{π} igg{log f_{θ}(u_j,λ) + frac{I_N(u_j, λ)}{f_{θ}(u_j,λ)}igg},dλ

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,…,M and λ the Fourier frequencies in the block (2,π,k/N, k = 1,…, N).

Author(s)

Ricardo Olea <raolea@uc.cl>

References

Dahlhaus, R. Fitting time series models to nonstationary processes. The Annals of Statistics. 1997; Vol. 25, No. 1:1-37.

Olea R, Palma W. An efficient estimator for locally stationary gaussian long-memory processes. The Annals of Statistics. 2010; Vol. 38, No. 5:2958-2997.