class_docstr: Filter a times series using the Baxter-King filter.
  
  This is a wrapper around the `bkfilter` function from `statsmodels`.
  (see `statsmodels.tsa.filters.bk_filter.bkfilter`).
  
  The Baxter-King filter is intended for economic and econometric time series
  data and deals with the periodicity of the business cycle. Applying their
  band-pass filter to a series will produce a new series that does not contain
  fluctuations at a higher or lower frequency than those of the business cycle.
  Baxter-King follow Burns and Mitchell's work on business cycles, which suggests
  that U.S. business cycles typically last from 1.5 to 8 years.
  
  Parameters
  ----------
  low : float
      Minimum period for oscillations. Baxter and King recommend a value of 6
      for quarterly data and 1.5 for annual data.
  
  high : float
      Maximum period for oscillations. BK recommend 32 for U.S. business cycle
      quarterly data and 8 for annual data.
  
  K : int
      Lead-lag length of the filter. Baxter and King suggest a truncation
      length of 12 for quarterly data and 3 for annual data.
  
  Notes
  -----
  Returns a centered weighted moving average of the original series.
  
  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
  --------
  >>> from sktime.transformations.series.bkfilter import BKFilter # doctest: +SKIP
  >>> import pandas as pd # doctest: +SKIP
  >>> import statsmodels.api as sm # doctest: +SKIP
  >>> dta = sm.datasets.macrodata.load_pandas().data # doctest: +SKIP
  >>> index = pd.date_range(start='1959Q1', end='2009Q4', freq='Q') # doctest: +SKIP
  >>> dta.set_index(index, inplace=True) # doctest: +SKIP
  >>> bk = BKFilter(6, 24, 12) # doctest: +SKIP
  >>> cycles = bk.fit_transform(X=dta[['realinv']]) # doctest: +SKIP
code: def __init__(
      self,
      low=6,
      high=32,
      K=12,
  ):
      self.low = low
      self.high = high
      self.K = K
      super().__init__()
  
imports: import pandas
  from sktime.transformations.base import BaseTransformer
label_desc: Use image node_id 1 to create a new BKFilter object from inherited base classes: BaseTransformer with example: obj = BKFilter(low, high, K)