This function makes use Reisen (1994) estimator to estimate the memory parameter d in the ARFIMA(p,d,q) model. It is based on the regression equation using the smoothed periodogram function as an estimate of the spectral density.
fdSperio(x, bandw.exp = 0.5, beta = 0.9)
a list with components
Sperio estimate
asymptotic standard deviation
standard error deviation
univariate time series data.
numeric: exponent of the bandwidth used in the regression equation.
numeric: exponent of the bandwidth used in the lag Parzen window.
Valderio A. Reisen valderio@cce.ufes.br and Artur J. Lemonte
The function also provides the asymptotic standard deviation and the standard error deviation of the fractional estimator.
The bandwidths are bw = trunc(n ^ bandw.exp)
, where 0 < bandw.exp < 1
and n is the sample size. Default bandw.exp= 0.5
;
and bw2 = trunc(n ^ beta)
, where 0 < beta < 1 and n is the
sample size. Default beta = 0.9
.
Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. Journal of Time Series Analysis 4(4), 221--238.
Reisen, V. A. (1994) Estimation of the fractional difference parameter in the ARFIMA(p,d,q) model using the smoothed periodogram. Journal Time Series Analysis, 15(1), 335--350.
Reisen, V. A., B. Abraham, and E. M. M. Toscano (2001) Parametric and semiparametric estimations of stationary univariate ARFIMA model. Brazilian Journal of Probability and Statistics 14, 185--206.
fdGPH
, fracdiff
memory.long <- fracdiff.sim(1500, d = 0.3)
spm <- fdSperio(memory.long$series)
str(spm, digits=6)
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