{smcl}
{* 23oct2004}{...}
{hline}
help for {hi:bking}
{hline}

{title:Apply Baxter-King band pass filter to time series}

{p 8 17}{cmd:bking}
{it:varlist}
[{cmd:if} {it:exp}]
[{cmd:in} {it:range}] 
{cmd:,} {cmdab:plo(}{it:#}{cmd:)}
{cmdab:phi(}{it:#}{cmd:)}
{cmdab:stub(}{it:abbrev}{cmd:)}
[
{cmdab:k(}{it:#}{cmd:)}
]

{p 4 4}You must {cmd:tsset} your data before using {cmd:bking}; see help {cmd: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 {cmd:by} prefix. {p_end}

{p 4 4}{cmd:varlist} may contain time-series operators; see help {cmd:varlist}. {p_end}

{p 4 4}{cmd:bking} filters one or more time series using the Baxter-King symmetric band-pass filter described in Baxter and King (1995).
The {cmd:plo()} and {cmd:phi()} arguments specify the minimum period of oscillation and 
maximum period of oscillation of the desired component of the time series, where 
2 < {it:plo} < {it:phi} < infinity. 
The "Burns-Mitchell" settings for this filter, applied to quarterly data, are 6 and 32 
quarters, with {it:k}=12.  {p_end}

{title:Options}
    
{p 4 8}{cmd:plo(}{it:#}{cmd:)} and {cmd:phi(}{it:#}{cmd:)} specify the minimum and maximum 
period of oscillation to be retained in the time series, and must be given. For quarterly 
data, common values are 6 and 32, which preserve the components of the data with period 
between 1.5 and 8.0 years, with {it:k}=12 (which loses three years' data from each end of the 
filtered series). For monthly data, 
common values are 18 and 96, which preserves the component of the data
with period between 1.5 and 8.0 years. For annual data, common values are 
2 and 8, with {it:k}=3.

{p 4 8}{cmd:stub(}{it:abbrev}{cmd:)}, which must be provided, specifies the "stub" from 
which new variable names will be created. Variables created by {cmd:stub} must be new 
variables. If the {it:varlist} contains time-series 
operators, the dots in their names are replaced by underscores so that the resulting 
new variables' names are legal. The first and last {it:k} observations
of the selected range are lost by {cmd:bking}, and those observations are set
to missing values in the filtered series.

{p 4 8}{cmd:k(}{it:#}{cmd:)} specifies the lead-lag length of the filter. This many 
observations will be lost at each end of the filtered series. If not specified, 
{cmd:k} is set to 12 (Baxter and King's recommended value for quarterly data).

{title:Examples}

{p 4 8}{stata "webuse lutkepohl,clear" :. webuse lutkepohl,clear}{p_end}

{p 4 8}{stata "bking investment, plo(6) phi(32) stub(F)" :. bking investment, plo(6) phi(32) stub(F)}{p_end}

{p 4 8}{stata "bking investment income consumption, plo(6) phi(32) k(8) stub(filt)" :. bking investment income consumption, plo(6) phi(32) k(8) stub(filt)}{p_end}

{p 4 8}{stata "bking D.investment, plo(4) phi(12) stub(fl)" :. bking D.investment, plo(4) phi(12) stub(fl)}{p_end}

{p 4 8}{stata "use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear":. use http://fmwww.bc.edu/ec-p/data/hayashi/sheston91.dta,clear}{p_end}

{p 4 8}{stata "drop if country>4":. drop if country>4}{p_end}

{p 4 8}{stata "tsset":. tsset}{p_end}

{p 4 8}{stata "by country:bking rgdppc, plo(2) phi(8) stub(SBY) k(3)":. by country:bking rgdppc, plo(2) phi(8) stub(SBY) k(3)}{p_end}


{title:Authors}

{p 4 4}Christopher F. Baum, Boston College, USA{break} 
       baum@bc.edu
       
{p 4 4}Martha Lopez, Boston College, USA{break} 
       lopezmo@bc.edu

{title:References}

{p}Marianne Baxter and Robert G. King, Measuring Business Cycles: Approximate
    Band-Pass Filters for Economic Time Series. Review of Economics and Statistics,
    1999, 81(4), 575-593. {p_end}

{p}Lawrence J. Christiano and Terry J. Fitzgerald, The Band Pass Filter, International
Economic Review, 2003, 44(2), 435-465.{p_end}
    
{p}Pawel Kowal (2005). MATLAB implementation of commonly used filters,
http://ideas.repec.org/c/wpa/wuwppr/0507001.html{p_end}

{title:Acknowledgements} 

{p 4 4}The Mata code of this routine was translated from MATLAB code made available by Pawel Kowal (2005).

{title:Also see}

{p 4 13}On-line: {help hprescott} (if installed), {help cfitzrw} (if installed), {help tsset}