{smcl}
{* 23oct2004}{...}
{hline}
help for {hi:cfitzrw}              SSC distribution 30 June 2006
{hline}

{title:Apply Christiano-Fitzgerald Random Walk band pass filter to time series}

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


{p 4 4}You must {cmd:tsset} your data before using {cmd:cfitzrw}; 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:cfitzrw} filters one or more time series using the  Christiano-Fitzgerald 
Random Walk band-pass filter described in  Christiano and Fitzgerald (2003).
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. 
 {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. 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.

{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. 

{title:Examples}

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

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

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

{p 4 8}{stata "cfitzrw D.investment, plo(4) phi(12) stub(fl)" :. cfitzrw 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: cfitzrw rgdppc, plo(2) phi(8) stub(SBY)":. by country: cfitzrw rgdppc, plo(2) phi(8) stub(SBY)}{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}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 bking} (if installed), {help tsset}