import numpy as np
from statsmodels.tools.validation import PandasWrapper, array_like
# 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
The 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_like
The features of x between the periodicities low and high.
trend : array_like
The trend in the data with the cycles removed.
See Also
--------
statsmodels.tsa.filters.bk_filter.bkfilter
Baxter-King filter.
statsmodels.tsa.filters.bk_filter.hpfilter
Hodrick-Prescott filter.
statsmodels.tsa.seasonal.seasonal_decompose
Decompose a time series using moving averages.
statsmodels.tsa.seasonal.STL
Season-Trend decomposition using LOESS.
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-'])
>>> plt.show()
.. plot:: plots/cff_plot.py
"""
#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")
pw = PandasWrapper(x)
x = array_like(x, 'x', ndim=2)
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] + np.dot(Bj[1:-i - 2].T, x[i + 1:-1]) +
B * x[-1] + np.dot(Bj[1:i].T, x[1:i][::-1]) + A * x[0])
y = y.squeeze()
cycle, trend = y.squeeze(), x.squeeze() - y
return pw.wrap(cycle, append='cycle'), pw.wrap(trend, append='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)