Source code for statsmodels.tsa.filters.bk_filter

from __future__ import absolute_import

import numpy as np
from scipy.signal import fftconvolve
from ._utils import _maybe_get_pandas_wrapper

[docs]def bkfilter(X, low=6, high=32, K=12): """ Baxter-King bandpass filter Parameters ---------- X : array-like A 1 or 2d ndarray. If 2d, variables are assumed to be in columns. low : float Minimum period for oscillations, ie., Baxter and King suggest that the Burns-Mitchell U.S. business cycle has 6 for quarterly data and 1.5 for annual data. high : float Maximum period for oscillations BK suggest that the U.S. business cycle has 32 for quarterly data and 8 for annual data. K : int Lead-lag length of the filter. Baxter and King propose a truncation length of 12 for quarterly data and 3 for annual data. Returns ------- Y : array Cyclical component of X References ---------- :: Baxter, M. and R. G. King. "Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series." *Review of Economics and Statistics*, 1999, 81(4), 575-593. Notes ----- Returns a centered weighted moving average of the original series. Where the weights a[j] are computed :: a[j] = b[j] + theta, for j = 0, +/-1, +/-2, ... +/- K b[0] = (omega_2 - omega_1)/pi b[j] = 1/(pi*j)(sin(omega_2*j)-sin(omega_1*j), for j = +/-1, +/-2,... and theta is a normalizing constant :: theta = -sum(b)/(2K+1) Examples -------- >>> import statsmodels.api as sm >>> import pandas as pd >>> dta = sm.datasets.macrodata.load_pandas().data >>> dates = sm.tsa.datetools.dates_from_range('1959Q1', '2009Q3') >>> index = pd.DatetimeIndex(dates) >>> dta.set_index(index, inplace=True) >>> cycles = sm.tsa.filters.bkfilter(dta[['realinv']], 6, 24, 12) >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> cycles.plot(ax=ax, style=['r--', 'b-']) >>> plt.show() .. plot:: plots/bkf_plot.py """ #TODO: change the docstring to ..math::? #TODO: allow windowing functions to correct for Gibb's Phenomenon? # adjust bweights (symmetrically) by below before demeaning # Lancosz Sigma Factors np.sinc(2*j/(2.*K+1)) _pandas_wrapper = _maybe_get_pandas_wrapper(X, K, K) X = np.asarray(X) omega_1 = 2.*np.pi/high # convert from freq. to periodicity omega_2 = 2.*np.pi/low bweights = np.zeros(2*K+1) bweights[K] = (omega_2 - omega_1)/np.pi # weight at zero freq. j = np.arange(1,int(K)+1) weights = 1/(np.pi*j)*(np.sin(omega_2*j)-np.sin(omega_1*j)) bweights[K+j] = weights # j is an idx bweights[:K] = weights[::-1] # make symmetric weights bweights -= bweights.mean() # make sure weights sum to zero if X.ndim == 2: bweights = bweights[:,None] X = fftconvolve(X, bweights, mode='valid') # get a centered moving avg/ # convolution if _pandas_wrapper is not None: return _pandas_wrapper(X) return X