Geweke and Porter-Hudak Estimator for ARFIMA(p,d,q)

Estimate the fractional (or “memory”) parameter \(d\) in the ARFIMA(p,d,q) model by the method of Geweke and Porter-Hudak (GPH). The GPH estimator is based on the regression equation using the periodogram function as an estimate of the spectral density.

Usage

fdGPH(x, bandw.exp = 0.5)

Arguments

x

univariate time series

bandw.exp

the bandwidth used in the regression equation

Details

The function also provides the asymptotic standard deviation and the standard error deviation of the fractional estimator.

The bandwidth is bw = trunc(n ^ bandw.exp), where 0 < bandw.exp < 1 and n is the sample size. Default bandw.exp = 0.5.

Value

d

GPH estimate

sd.as

asymptotic standard deviation

sd.reg

standard error deviation

References

see those in fdSperio.

Author

Valderio A. Reisen and Artur J. Lemonte

See also

fdSperio, fracdiff

Examples

memory.long <- fracdiff.sim(1500, d = 0.3)
fdGPH(memory.long$series)
#> $d
#> [1] 0.3165372
#> 
#> $sd.as
#> [1] 0.1212815
#> 
#> $sd.reg
#> [1] 0.1272886
#>