On Sat, 19 Jul 2014, Sven Schreiber wrote: I bet you VAR is very close to the non-stationarity reason. Typically, these things happen because finite sample estimates are badly biased towards zero. Kilian's bias correction helps, but only up to a point, since it contains a mechanism for ensuring that the bias correction does not introduce unstable roots in the VAR, so in practice if your data are very persistent and there's at least a near-unit eigenvalue in your companion matrix, there's little you can do. The script below sort-of exemplifies the issue in the univariate case (I know it's trivial, but in fact it shows what the issue is quite clearly). <hansl> set echo off set messages off nulldata 256 phi = 0.95 # generate data series x = 0 x = phi*x(-1) + normal() # now estimate a "VAR" ols x 0 x(-1) --quiet phihat = $coeff[2] # typically, this is biased towards 0 series u = $uhat # bootstrap! scalar boot_rep = 199 matrix phiboot = zeros(boot_rep,1) loop i=1..boot_rep --quiet ub = resample(u) series xb = 0 xb = phihat*x(-1) + ub ols xb 0 xb(-1) --quiet phiboot[i] = $coeff[2] endloop cb = quantile(phiboot, {0.05, 0.95}) printf "phihat = %g\n", phihat printf "95%% cb = %g - %g\n", cb[1], cb[2] </hansl> ------------------------------------------------------- Riccardo (Jack) Lucchetti Dipartimento di Scienze Economiche e Sociali (DiSES) Università Politecnica delle Marche (formerly known as Università di Ancona) r.lucchetti(a)univpm.it http://www2.econ.univpm.it/servizi/hpp/lucchetti -------------------------------------------------------