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 |

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 residuals RSS = sum(ALLRESIDUALS^2) 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