statsmodels.sandbox.tsa.fftarma.ArmaFft¶
-
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.
Notes
TODO: check whether we do not 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
Methods
acf
([lags])Theoretical autocorrelation function of an ARMA process.
acf2spdfreq
(acovf[, nfreq, w])not really a method just for comparison, not efficient for large n or long acf
acovf
([nobs])Theoretical autocovariance function of ARMA process.
arma2ar
([lags])A finite-lag AR approximation of an ARMA process.
arma2ma
([lags])A finite-lag approximate MA representation of an ARMA process.
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
from_coeffs
([arcoefs, macoefs, nobs])Create ArmaProcess from an ARMA representation.
from_estimation
(model_results[, nobs])Create an ArmaProcess from the results of an ARMA estimation.
generate_sample
([nsample, scale, distrvs, …])Simulate data from an ARMA.
impulse_response
([leads])Compute the impulse response function (MA representation) for ARMA process.
invertroots
([retnew])Make MA polynomial invertible by inverting roots inside unit circle.
invpowerspd
(n)autocovariance from spectral density
pacf
([lags])Theoretical partial autocorrelation function of an ARMA process.
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 function that is a method, no self used
periodogram
([nobs])Periodogram for ARMA process given by lag-polynomials ar and ma.
plot4
([fig, nobs, nacf, nfreq])Plot results
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
spdshift
(n)power spectral density using fftshift
Properties
Roots of autoregressive lag-polynomial
Arma process is invertible if MA roots are outside unit circle.
Arma process is stationary if AR roots are outside unit circle.
Roots of moving average lag-polynomial