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help for ^fracirf^                 (SSC distribution 11 October 2000)
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Compute impulse response function for fractionally-integrated timeseries
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^fracirf^  newvarname  D[real] [, ^AR^(numlist) ^MA^(numlist) ^CUM^(newvarname)] 


Description
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^fracirf^ computes an approximation to the infinite moving average 
representation (or impulse response function) of a 
fractionally-integrated timeseries, given a value of the fractional 
integration (long memory) parameter ^d^ and, optionally, values of p 
autoregressive and q moving average parameters corresponding to an 
ARFIMA(p,d,q) representation. If a series is fractionally integrated, 
it is neither stationary (I[0]) nor is it a unit root (I{1}) process; 
it is an I(d) process, with d a real number. An excellent survey of 
long memory models--which originated in hydrology, and have been widely 
applied in economics and finance--is given by Baillie (1996). 

Once one of several available estimators has been used to determine the
^d^ value for a timeseries (and optionally the ^AR^ and/or ^MA^ parameters
corresponding to the ARFIMA representation estimated by an exact maximum
likelihood routine), ^fracirf^ may be used to generate the infinite 
moving average representation, or impulse response function (IRF), 
of the series. The computation follows Theorem 11.10 of Gourieroux and 
Monfort (1997, p. 438). The number of points at which the IRF will be 
computed equals the number of observations in the current sample.

Options
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The ^AR^ and ^MA^ options are used to provide the estimated parameters 
of the ARFIMA model.

The ^CUM(newvarname)^ option is used if both the IRF and its cumulation
are required. For instance, if the series from which a long-memory model
has been estimated is the first difference of the original data, the
cumulative series will be the IRF for the original timeseries.

Examples
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	. ^set obs 100^
	. ^fracirf irf1, d(0.42) ar(0.6 0.3) ma(0.2 -0.1)^
	
	. ^use http://fmwww.bc.edu/ec-p/data/Mills2d/fta.dta^
	. ^gphudak D.ftap^
	. ^fracirf irf2,d(`r(gph)')^
	. ^gphudak D.ftap^
	. ^fracirf irf3,d(`r(gph)') cum(cumirf)^


References
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Baillie, R., Long Memory Processes and Fractional Integration in 
      Econometrics, Journal of Econometrics, 73, 1996, 5-59.
      
Gourieroux, Christian and Monfort, Alain, Time Series and
      Dynamic Models, 1997. Cambridge: Cambridge University Press.


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

        
Also see
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On-line:  help for @tsset@, @gphudak@ (if installed), @modlpr@ (if installed),
          @roblpr@ (if installed), @lomodrs@ (if installed), @fracdiff@ 
          (if installed)