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help for butterworth              SSC distribution 03 July 2006
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Apply Butterworth square-wave highpass filter to time series

        butterworth varlist [if exp] [in range] , freq(#) stub(abbrev) [
                 order(#) ]


    You must tsset your data before using butterworth; see help tsset.  If a
    panel calendar is in effect, the filter can be applied if a single panel is
    specified using if or in qualifiers, or with the by prefix.

    varlist may contain time-series operators; see help varlist.

    butterworth filters one or more time series using the Butterworth
    square-wave highpass filter described in Pollock (2000).  The freq()
    argument specifies the minimum period of oscillation of the desired
    component of the time series, where 2 < freq < infinity. The order() of the
    filter may also be chosen; if not specified, it defaults to 2.

Options
    
    freq(#) specifies the minimum period of oscillation, in periods per cycle,
        to be retained in the time series, and must be given. It must be
        greater than 2 (the reciprocal of the Nyquist frequency).
        Higher-frequency components of the series will be returned in the
        filtered series.

    stub(abbrev), which must be provided, specifies the "stub" from which new
        variable names will be created. Variables created by stub must be new
        variables. If the varlist contains time-series operators, the dots in
        their names are replaced by underscores so that the resulting new
        variables' names are legal.

    order(#) specifies the order of the filter. If not specified, it defaults
        to 2.

Examples

    . webuse lutkepohl,clear

    . butterworth investment, freq(6) phi stub(F)

    . butterworth investment income consumption, freq(12) stub(filt)

    . butterworth D.investment, freq(4) order(3) stub(fl)

    . use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear

    . drop if country>4

    . tsset

    . by country: butterworth rgdppc, freq(3) stub(SBY)


Authors

    Christopher F. Baum, Boston College, USA
    baum@bc.edu

    Martha Lopez, Boston College, USA
    lopezmo@bc.edu

References

D.S.G. Pollock, Trend estimation and de-trending via rational square-wave
filters, Journal of Econometrics, 2000, 99, 317-334.
    
Pawel Kowal (2005). MATLAB implementation of commonly used filters,
http://ideas.repec.org/c/wpa/wuwppr/0507001.html

Acknowledgements 

    The Mata code of this routine was translated from MATLAB code made
    available by Pawel Kowal (2005).

Also see

    On-line: hprescott (if installed), bking (if installed), cfitzrw (if
             installed), tsset