Fractionally Differenciate Data
Differenciates the time series data using the approximated binomial expression of the long-memory filter and an estimate of the memory parameter in the ARFIMA(p,d,q) model.
diffseries(x, d)
x |
numeric vector or univariate time series. |
d |
number specifiying the fractional difference order. |
Since 2018, we are using (an important correction of) the fast
algorithm based on the discrete Fourier transform (fft)
by Jensen and Nielsen which is significantly faster for large
n = length(x).
the fractionally differenced series x.
Valderio A. Reisen valderio@cce.ufes.br and Artur
J. Lemonte (first slow version), now hidden as diffseries.0().
Current version: Jensen and Nielsen (2014); tweaks by Martin Maechler, 2018.
See those in fdSperio; additionally
Reisen, V. A. and Lopes, S. (1999) Some simulations and applications of forecasting long-memory time series models; Journal of Statistical Planning and Inference 80, 269–287.
Reisen, V. A. Cribari-Neto, F. and Jensen, M.J. (2003) Long Memory Inflationary Dynamics. The case of Brazil. Studies in Nonlinear Dynamics and Econometrics 7(3), 1–16.
Jensen, Andreas Noack and Nielsen, Morten Ørregaard (2014) A Fast Fractional Difference Algorithm. Journal of Time Series Analysis 35(5), 428–436; doi: 10.1111/jtsa.12074.
memory.long <- fracdiff.sim(80, d = 0.3) str(mGPH <- fdGPH(memory.long$series)) r <- diffseries(memory.long$series, d = mGPH$d) #acf(r) # shouldn't show structure - ideally
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