Source code for statsmodels.tsa.filters.cf_filter

from statsmodels.compat.python import range

import numpy as np
from ._utils import _maybe_get_pandas_wrapper

# the data is sampled quarterly, so cut-off frequency of 18

# Wn is normalized cut-off freq
#Cutoff frequency is that frequency where the magnitude response of the filter
# is sqrt(1/2.). For butter, the normalized cutoff frequency Wn must be a
# number between  0 and 1, where 1 corresponds to the Nyquist frequency, p
# radians per sample.

#NOTE: uses a loop, could probably be sped-up for very large datasets
[docs]def cffilter(X, low=6, high=32, drift=True): """ Christiano Fitzgerald asymmetric, random walk filter Parameters ---------- X : array-like 1 or 2d array to filter. If 2d, variables are assumed to be in columns. low : float Minimum period of oscillations. Features below low periodicity are filtered out. Default is 6 for quarterly data, giving a 1.5 year periodicity. high : float Maximum period of oscillations. Features above high periodicity are filtered out. Default is 32 for quarterly data, giving an 8 year periodicity. drift : bool Whether or not to remove a trend from the data. The trend is estimated as np.arange(nobs)*(X[-1] - X[0])/(len(X)-1) Returns ------- cycle : array The features of `X` between periodicities given by low and high trend : array The trend in the data with the cycles removed. Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.macrodata.load_pandas().data >>> index = pd.DatetimeIndex(start='1959Q1', end='2009Q4', freq='Q') >>> dta.set_index(index, inplace=True) >>> cf_cycles, cf_trend = sm.tsa.filters.cffilter(dta[["infl", "unemp"]]) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> cf_cycles.plot(ax=ax, style=['r--', 'b-']) >>> .. plot:: plots/ See Also -------- statsmodels.tsa.filters.bk_filter.bkfilter statsmodels.tsa.filters.hp_filter.hpfilter statsmodels.tsa.seasonal.seasonal_decompose """ #TODO: cythonize/vectorize loop?, add ability for symmetric filter, # and estimates of theta other than random walk. if low < 2: raise ValueError("low must be >= 2") _pandas_wrapper = _maybe_get_pandas_wrapper(X) X = np.asanyarray(X) if X.ndim == 1: X = X[:,None] nobs, nseries = X.shape a = 2*np.pi/high b = 2*np.pi/low if drift: # get drift adjusted series X = X - np.arange(nobs)[:,None]*(X[-1] - X[0])/(nobs-1) J = np.arange(1,nobs+1) Bj = (np.sin(b*J)-np.sin(a*J))/(np.pi*J) B0 = (b-a)/np.pi Bj = np.r_[B0,Bj][:,None] y = np.zeros((nobs,nseries)) for i in range(nobs): B = -.5*Bj[0] -np.sum(Bj[1:-i-2]) A = -Bj[0] - np.sum(Bj[1:-i-2]) - np.sum(Bj[1:i]) - B y[i] = Bj[0] * X[i] +[1:-i-2].T,X[i+1:-1]) + B*X[-1] + \[1:i].T, X[1:i][::-1]) + A*X[0] y = y.squeeze() cycle, trend = y, X.squeeze()-y if _pandas_wrapper is not None: return _pandas_wrapper(cycle), _pandas_wrapper(trend) return cycle, trend
if __name__ == "__main__": import statsmodels as sm dta = sm.datasets.macrodata.load().data[['infl','tbilrate']].view((float,2))[1:] cycle, trend = cffilter(dta, 6, 32, drift=True) dta = sm.datasets.macrodata.load().data['tbilrate'][1:] cycle2, trend2 = cffilter(dta, 6, 32, drift=True)