On Sun, 13 May 2012, Sven Schreiber wrote: Well, not exactly two lines, but not overly difficult either: <hansl> set echo off set messages off function scalar gph(series y, scalar m) /* Geweke/Porter-Hudak estimator */ matrix f = fft({y})/$nobs matrix f = f[2:(m+1),] matrix f = log(sumr(f.^2)) matrix lambda = (pi/$nobs) * seq(1,m)' matrix X = ones(m,1) ~ log(sin(lambda)) matrix b = mols(f, X) return -0.5*b[2] end function # --- main ----------------------------------- # generate pseudorandom data set seed 1234 nulldata 1000 setobs 1 1 --special true_d = -0.25 true_phi = 0.7 true_theta = 0.4 u = fracdiff(normal(), -true_d) y = 3 + filter(u, {1, true_theta}, true_phi) # initialise parameters: preliminary estimate of d via GPH, the # rest via conditional ARMA d = gph(y, 30) my = mean(y) z = fracdiff(y - my, d) arma 1 1 ; z -cq phi = $coeff[2] theta = $coeff[3] b = my # do conditional mle printf "Initial values: phi = %f, theta = %f, d = %f\n", \ phi, theta, d mle ll = -0.5 * (ln(s2) + e2/s2) series e = filter(y - b, {1, -phi}, -theta) series e = abs(d) < 0.5 ? fracdiff(e, d) : NA series e2 = e^2 scalar s2 = mean(e2) params b phi theta d end mle </hansl> Note: the above will estimate the parameters of an arfima(1,d,1) model via *conditional* ml by making a number of choices that are both asymptotically valid and computationally convenient. In order to get *full* ml estimates you'd have to do much more work. IMHO, the _definitive_ implementation of full-ML arfima is Doornik's "arfima" ox package, which uses a very clever algorithm for fast computation of determinants and inverses of Toeplitz matrices which unfortunately we don't have yet. -------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti --------------------------------------------------