statsmodels.tsa.filters.bk_filter.bkfilter¶

statsmodels.tsa.filters.bk_filter.bkfilter(x, low=6, high=32, K=12)[source]¶

Filter a time series using the Baxter-King bandpass filter.

Parameters

xarray_like: A 1 or 2d ndarray. If 2d, variables are assumed to be in columns.
lowfloat: 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.
highfloat: Maximum period for oscillations BK suggest that the U.S. business cycle has 32 for quarterly data and 8 for annual data.
Kint: 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)

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()

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