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hannriss(x, pdq:vector(p,d,q) [,degree:d1] [,maxlag:m] \
   [,polish:T, cycles:nc] [,arsign:Arsign] [,masign:Masign]), integers
   p >= 0, d >= 0 q >= 0, m >= p + q, nc >= 0, d1, Arsign and Masign +1
   or -1

Keywords: arima models, time domain, preliminary estimation
hannriss(x,pdq:vector(p,d,q)), where p >= 0, d >= 0 and q >= 0 are
integers computes preliminary estimates of ARIMA coefficients using the
Hannan-Rissanen method.

The first step computes yulewalker estimates based on m autocorrelations
unless q = 0 when only p autocorrelations are used.  The default for m
is 20 + p + q.

Its value is structure(phi:phihat,theta:thetahat,xtxinv,rss:rss,nobs:n)

hannriss(x,pdq:vector(p,d,q),maxlag:m), integer m >= p + q, does the
same using m autocorrelations.

hannriss(x,pdq:vector(p,d,q),degree:d1 [,maxlag:m]) does the same,
except the possibly differenced data is detrended with a polynomial of
order d1.  d1 < 0 means nothing is subtracted.  The default for d1 is 0
when d = 0 and -1 when d > 0.

In addition to returning a value, hannriss() creates the following side
effect variables
  COEF = vector(phihat,thetahat)
  XTXINV = analogue of solve(X' %c% X) matrix in regression
  ALLRESIDUALS = residuals from fitted model including backcast
  NEG2LOGL = -2*log(likelihood)
  NPAR = p + q + degree1 + 1 = number of coefficients estimated
    where degree1 = max(d1,-1).

phi is defined so the autoregressive operator is Phi(B) = 1 +
Arsign*phi[1]*B + Arsign*phi[2]*B^2 + ... + Arsign*phi[p]*B^p.

theta is defined so that the moving average operator is Theta(B) = 1 +
Masign*theta[1]*B + Masign*theta[2]*B^2 + ... + Masign*theta[q]*B^q,
where B is the backshift operator.

The default values for Arsign and Masign are -1 and -1, but you may
change them by keyword phrases 'arsign:Arsign' and 'masign:Masign' or by
creating variables ARSIGN and/or MASIGN with values +1 or -1.  See topic
'MASIGNS' for details.

You can also include the following keyword phrases as arguments
  polish:T      carry out one or more extra "polishing" steps that
                should move the estimates closer to the unconditional
                least squares estimates.
  cycles:nc   nc > 0 polishing cycles will be carried out; default is 1

There is currently no provision for seasonal ARIMAs

Gary Oehlert 2003-01-15