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*
* @HannanRissanen( options ) series  start  end
*
* Computes estimates for an ARMA model using the Hannan-Rissanen algorithm, which
* runs a LS regression on lags of the dependent variable and residuals from a
* long preliminary AR.
*
* Parameters:
*   series      Series to analyze
*   start end   Range to analyze [range of series]
*
* Options
*   AR=number of AR parameters [0]
*   MA=number of MA parameters [0]
*   DIFF=number of regular differencings[0]
*   SDIFFS=number of seasonal differencings[0]
*   M=number of lags in the long preliminary AR. By default, this uses the
*     Gomez proposal of max(log**2(T),2*max(p,q))
*   METHOD=[YULE]/BURG
*     Method used in computing the long AR
*   [CORRECTION]/NOCORRECTION
*     Chooses whether or not to do a one-step correction to the initial estimates.
*   [PRINT]/NOPRINT
*   DEFINE=equation to define
*
* References:
*  Hannan and Rissanen, "Recursive estimation of mixed autoregressive-moving average order",
*   Biometrika, 1991, vol 69, pp 81-94.
*
*  Gomez and Maravall, "Automatic Modeling Methods for Univariate Series", in
*   Peña, Tiao and Tsay, eds., "A Course in Time Series Analysis", New York: Wiley, 2001.
*
procedure HannanRissanen series start end
type series  series
type integer start end
*
option integer   ar          0
option integer   ma          0
option integer   diffs       0
option integer   sdiffs      0
option integer   m
option switch    correction  1
option choice    method      1  yule burg
option switch    print       1
option equation *define
*
local  integer   startl endl lags nobs skips span
local  series    xc e v w
local  real      value
local  equation  armaeq
local  vector    beta0
*
if .not.%defined(series) {
   disp "Syntax: @HannanRissanen(options)  SERIES start end"
   return
}

compute span=2:1-1:1
inquire(series=series) startl<<start endl<<end
compute startl=startl+diffs+sdiffs*span
diff(diffs=diffs,sdiffs=sdiffs,center) series startl endl xc
compute nobs=endl-startl+1
*
*  By default, use Gomez proposal for lags in the AR
*
if .not.%defined(m)
   compute lags=%imax(fix(log(nobs)^2),2*%imax(ar,ma))
else
   compute lags=%imax(m,%imax(ar,ma))
*
* Compute the long AR
*
@DurbinLevinson(m=lags,method=method) series startl endl
*
set e startl endl = %if(t<startl+lags,0.0,%(value=xc,%do(j,1,lags,value=value-%beta(j)*xc{j}),value))
*
* If we're doing a correction step, use the data range that will be used in
* the correction step. This includes some extra zeros.
*
if correction
   compute skips=%imax(ar,ma)
else
   compute skips=lags+ma
linreg(define=armaeq,noprint) xc startl+skips endl
# xc{1 to ar} e{1 to ma}
compute beta0=%beta
*
* If <<correction>>, do one step of a Gauss-Newton algorithm on the maximum sample
* size that can be done by a LS regression. The definition of <<v>> below (which
* generates the derivatives with respect to the AR parameters) is more accurate than
* what is described in (e.g.) Gomez and Maravall. This, in fact, gives the exact
* derivatives of the <<e>> series as generated below with respect to the AR parameters.
*
if correction {
   set e startl endl = %if(t<startl+skips,0.0,xc-%dot(%beta,%eqnxvector(armaeq,t)))
   *
   *set v startl endl = %if(t<startl+skips,0.0,%(value=e,%do(j,1,ar,value=value+%beta(   j)*v{j}),-value))
   set v startl endl = value=xc,%do(j,1,ma,value=value+%beta(ar+j)*%if(t-j<startl,0,v{j})),-value
   set w startl endl = %if(t<startl+skips,0.0,%(value=e,%do(j,1,ma,value=value+%beta(ar+j)*w{j}),-value))
   *
   linreg(noprint) e startl+skips endl
   # v{1 to ar} w{1 to ma}
   compute %beta=beta0-%beta
}
*
modify armaeq define
if print {
   disp
   disp "Equation Estimated by Hannan-Rissanen"
}
vreplace(print=print) e with %mvgavge
end