Dear Allin, Thanks, that was exactly example that I was thinking of. All the best, Davor On 18.3.2011. 19:54, Allin Cottrell wrote:

Dear Allin I tried this simulation script about z-test years ago. It's a great idea. But I found that the result of this simulation depends on potential "initial effect" since the script generate variables in this way: ... series u = 0 ... series y = 0 To avoid the initial effect, the simulation would conventionally drop some initial samples and do tests for the rest. So I slightly modified your script to generate 130 sample per replication and dropped the first 30 sample to do your comparison as shown below. In shorts after dropping the first 30 samples, the AIC actually does a good job for (100 samples of this) AR(3) simulation; BIC and HQC select too short lags. Though the results are a little bit different for other ICs, a good news is that the z-test proposed in gretl seems more robust relatively. Yi-Nung Yang Dept. of International Business, Chung Yuan Christian University, Taiwan. The original script's result: ----------------------------------------------------------------------- 1000 replications, test down from 6 lags Lag order selected: mean on row 1, s.d. on row 2 AIC BIC HQC z-test 5.85 3.33 4.91 3.10 0.46 1.48 1.25 1.39 The result of dropping the first 30 samples: ----------------------------------------------------------------------- 1000 replications, test down from 6 lags Lag order selected: mean on row 1, s.d. on row 2 AIC BIC HQC z-test 3.01 1.97 2.44 3.18 1.16 0.91 0.99 1.38 The modified script by me: <script> nulldata 130 # seed so that experiment can be repeated exactly set seed 89675430 # params of error process: can set some to zero, but # here we do AR(3) scalar rho1 = 0.5 scalar rho2 = -0.3 scalar rho3 = 0.2 # y params: d = drift, a = autoregressive parameter scalar d = 0.02 scalar a = 0.9 # test down from scalar maxlag = 6 # test-recoding scalars scalar zval, pz, zlag, pzstar # replications scalar replics = 1000 # matrix to record results across relications matrix lsel = zeros(replics, 4) # outer loop: replications loop j=1..replics -q # build stationary AR(p) error process for u series u = 0 series e = normal() u = rho1*u(-1) + rho2*u(-2) + rho3*u(-3) + e # construct y series for "ADF testing" series y = 0 series y = d + a*y(-1) + u # difference for DF regression dy = diff(y) lags maxlag ; dy # comprehensive list of lagged differences list dyL = dy_* # Information Criterion matrix matrix IC = zeros(3, maxlag+1) zlag = 0 # inner loop: test for lag length loop for (i=maxlag; i>=0; i--) -q smpl 31 130 ols dy 0 y(-1) dyL -q IC[1,i+1] = $aic IC[2,i+1] = $bic IC[3,i+1] = $hqc if (i > 0 && zlag == 0) # we haven't yet found a significant "final lag" zval = abs($coeff(dy_$i)/$stderr(dy_$i)) pz = 2 * pvalue(z, zval) # printf "pz = %g\n", pz if (pz <= 0.10) zlag = i pzstar = pz endif endif if i > 0 # discard the last lag dyL -= dy_$i endif endloop # just for checking... # print IC matrix iCmin = iminr(IC) - 1 # Verbose printing to check results (set replics = 1) # matrix Cmin = minr(IC) # printf "AIC min = %8.3f at lag %d\n", Cmin[1], iCmin[1] # printf "BIC min = %8.3f at lag %d\n", Cmin[2], iCmin[2] # printf "HQC min = %8.3f at lag %d\n", Cmin[3], iCmin[3] # if zlag > 0 # printf "z p-val = %8.3f at lag %d\n", pzstar, zlag # else # print "z-test selects no lags" # endif lsel[j,1:3] = iCmin' lsel[j,4] = zlag endloop # Uncomment to print the full results # print lsel matrix stats = meanc(lsel) | sdc(lsel) colnames(stats, "AIC BIC HQC z-test") printf "\n%d replications, test down from %d lags\n", replics, maxlag print "Lag order selected: mean on row 1, s.d. on row 2" printf "\n%8.2f\n", stats </script> 2011/3/19 Allin Cottrell <cottrell(a)wfu.edu&gt;: