[Gretl-devel] arima initial values when P(L) is close to zero

Dear Allin, The file mentioned was attached in one of the recent messages gretl version 2018d-git Current session: 2018-11-15 22:29 ? set verbose off Read datafile /home/oleh/gretl/very_bad_data.gdt 'arima 2 1; var1 --x-12-arima' results: Model 1: ARMA, using observations 1900-1999 (T = 100) Estimated using X-13-ARIMA (exact ML) Dependent variable: var1             coefficient   std. error     z      p-value  ------------------------------------------------------  const       2.09907       2.62101     0.8009   0.4232  phi_1       0.347239      0.331677    1.047    0.2951  phi_2       0.608396      0.321796    1.891    0.0587  *  theta_1     0.558995      0.345076    1.620    0.1052 Mean dependent var   0.164128   S.D. dependent var   3.069430 Mean of innovations  0.028041   S.D. of innovations  0.975996 Log-likelihood      −140.8892   Akaike criterion     291.7784 Compare 'const' and 'Mean dependent var'! Initial values from failed 'arima 2 1; var1 --verbose': ARMA initialization: using linear AR model Iteration 1: loglikelihood = -176.101858631 Parameters:       426.94     0.91245    0.087320  0.00010000 It seems, this is how the figures above were obtained: Estimate 'ols var1 0 var1(-1 to -2)' Then (b[1]/(1-sum(b[-1]))|b[-1])' is      426.94      0.91245     0.087320 But P(1), i.e. 1 - sum(b[-1]) = 0.000224941 Naturally, with such an initial constant eventually we get: Iteration 999: loglikelihood = -145.834755022 (steplength = 1) Parameters:       339.16     0.43512     0.56488     0.48653 Gradients:    -0.0029644     -265.26     -265.19   -0.071660 (norm 8.16e+00) --- FINAL VALUES: loglikelihood = -145.828634454 (steplength = 1) Parameters:       336.15     0.40383     0.59616     0.52404 Gradients:    -0.0029303     -2808.7     -2808.0    -0.69924 (norm 2.65e+01) The convergence criterion was not met Obviously, it takes a couple of minutes to change regression_costant/P(1) for mean(y), or change only when, say P(1)<0.15 Code to reproduce set verbose off open very_bad_data.gdt --quiet printf "\n'arima 2 1; var1 --x-12-arima' results:\n" outfile mybuf --buffer --quiet arima 2 1; var1 --x-12-arima end outfile smallbuf = substr(mybuf,1,strlen(mybuf)-strlen(strstr(mybuf,"Schwarz criterion"))) print smallbuf printf "\nCompare 'const' and 'Mean dependent var'!\n" outfile mybuf --buffer --quiet catch arima 2 1; var1 --verbose end outfile err = $error smallbuf = substr(mybuf,1,strlen(mybuf)-strlen(strstr(mybuf,"Gradients:"))) endbuf = strstr(mybuf,"Iteration 999:") printf "\nInitial values from failed 'arima 2 1; var1 --verbose':" printf "\n%s", smallbuf printf "\nIt seems, this is how the figures above were obtained:\n" printf "\nEstimate 'ols var1 0 var1(-1 to -2)'\n" ols var1 0 var1(-1 to -2) --quiet b = $coeff printf "\nThen (b[1]/(1-sum(b[-1]))|b[-1])' is \n\n" eval (b[1]/(1-sum(b[-1]))|b[-1])' printf "\nBut P(1), i.e. 1 - sum(b[-1]) = %g\n\n",(1 -sum(b[-1])) printf "Naturally, with such an initial constant eventually we get:\n\n" print endbuf eval errmsg(err) Oleh