class statsmodels.sandbox.tsa.fftarma.ArmaFft(ar, ma, n)[source]

fft tools for arma processes

This class contains several methods that are providing the same or similar returns to try out and test different implementations.


TODO: check whether we don’t want to fix maxlags, and create new instance if maxlag changes. usage for different lengths of timeseries ? or fix frequency and length for fft

check default frequencies w, terminology norw n_or_w

some ffts are currently done without padding with zeros

returns for spectral density methods needs checking, is it always the power spectrum hw*hw.conj()

normalization of the power spectrum, spectral density: not checked yet, for example no variance of underlying process is used


acf2spdfreq(acovf[, nfreq, w]) not really a method
fftar([n]) Fourier transform of AR polynomial, zero-padded at end to n
fftarma([n]) Fourier transform of ARMA polynomial, zero-padded at end to n
fftma(n) Fourier transform of MA polynomial, zero-padded at end to n
filter(x) filter a timeseries with the ARMA filter
filter2(x[, pad]) filter a time series using fftconvolve3 with ARMA filter
invpowerspd(n) autocovariance from spectral density
pad(maxlag) construct AR and MA polynomials that are zero-padded to a common length
padarr(arr, maxlag[, atend]) pad 1d array with zeros at end to have length maxlag
plot4([fig, nobs, nacf, nfreq])
spd(npos) raw spectral density, returns Fourier transform
spddirect(n) power spectral density using padding to length n done by fft
spdmapoly(w[, twosided]) ma only, need division for ar, use LagPolynomial
spdpoly(w[, nma]) spectral density from MA polynomial representation for ARMA process
spdroots(w) spectral density for frequency using polynomial roots
spdroots_(arroots, maroots, w) spectral density for frequency using polynomial roots
spdshift(n) power spectral density using fftshift


arroots Roots of autoregressive lag-polynomial
isinvertible Arma process is invertible if MA roots are outside unit circle
isstationary Arma process is stationary if AR roots are outside unit circle
maroots Roots of moving average lag-polynomial