# Source code for statsmodels.tsa.filters.bk_filter

import numpy as np
from scipy.signal import fftconvolve

from statsmodels.tools.validation import array_like, PandasWrapper

[docs] def bkfilter(x, low=6, high=32, K=12): """ Filter a time series using the 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 ------- ndarray The cyclical component of x. See Also -------- statsmodels.tsa.filters.cf_filter.cffilter The Christiano Fitzgerald asymmetric, random walk 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. 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) See the notebook `Time Series Filters <../examples/notebooks/generated/tsa_filters.html>`__ for an overview. 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. 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) >>> 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)) pw = PandasWrapper(x) x = array_like(x, 'x', maxdim=2) 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 return pw.wrap(x, append='cycle', trim_start=K, trim_end=K)

Last update: Apr 12, 2024