gretl version 2018c
Current session: 2018-10-26 14:50
? eval $sysinfo
bundle anonymous:
nproc = 4
blascore = Atom
hostname = DESKTOP-DE5ESQO
os = windows
mpi = 0
blas = openblas
omp_num_threads = 4
omp = 1
blas_parallel = OpenMP
mpimax = 4
wordlen = 32
? open bad_data.gdt
Read datafile C:\Users\Lenovo\Documents\gretl\bad_data.gdt
periodicity: 4, maxobs: 204
observations range: 1950:1 to 2000:4
Listing 4 variables:
0) const 1) diff_series 2) y_one 3) y_two
? smpl 1 194
Full data range: 1950:1 - 2000:4 (n = 204)
Current sample: 1950:1 - 1998:2 (n = 194)
? series sty=diff_series/sd(diff_series)
Generated series sty (ID 4)
? list zli = y_one y_two
Generated list zli
? y = sty+6.48
Generated series y (ID 5)
? arima 3 0 0; 1 0 0; y 0 zli --verbose
ARMA initialization: using nonlinear AR model
Iteration 1: loglikelihood = -136.938951717
Parameters: 6.4637 0.58059 -0.11046 -0.082556 -0.093679 0.10601
-1.9068
Gradients: 9.2712 10.471 1.3218 -2.0031 -2.1470 3.9715
-2.8401 (norm 3.22e+000)
Iteration 2: loglikelihood = -136.689823002 (steplength = 0.0016)
Parameters: 6.4785 0.59734 -0.10835 -0.085761 -0.097114 0.11237
-1.9113
Gradients: 3.7130 3.7662 -2.9409 -3.1750 -1.7423 -1.1818
-2.5919 (norm 2.14e+000)
Iteration 3: loglikelihood = -136.635783208 (steplength = 0.0016)
Parameters: 6.4839 0.60234 -0.11626 -0.092855 -0.10056 0.10774
-1.9166
Gradients: 1.9617 4.8733 1.0840 1.5885 1.2310 3.6716
-0.80868 (norm 1.60e+000)
Iteration 4: loglikelihood = -136.600859241 (steplength = 0.008)
Parameters: 6.4784 0.61437 -0.13175 -0.090207 -0.091373 0.11082
-1.9254
Gradients: 3.9294 3.0305 2.2406 1.5760 0.43245 2.7506
-0.97313 (norm 2.07e+000)
Iteration 5: loglikelihood = -136.590682758 (steplength = 0.008)
Parameters: 6.4844 0.61344 -0.13942 -0.082111 -0.082786 0.11045
-1.9365
Gradients: 1.7762 4.1148 3.1480 0.21233 -0.75300 3.1392
-1.2209 (norm 1.57e+000)
Iteration 6: loglikelihood = -136.579257175 (steplength = 0.008)
Parameters: 6.4832 0.61301 -0.13869 -0.079072 -0.080908 0.11078
-1.9511
Gradients: 2.1798 3.8598 2.7328 -0.11127 -0.24403 3.3903
-0.55423 (norm 1.62e+000)
Iteration 7: loglikelihood = -136.558904481 (steplength = 0.04)
Parameters: 6.4846 0.59869 -0.13673 -0.098319 -0.057675 0.13257
-1.9918
Gradients: 1.7338 3.3469 1.7212 0.78241 -1.7498 3.2189
-0.55661 (norm 1.47e+000)
Iteration 8: loglikelihood = -136.521260314 (steplength = 0.04)
Parameters: 6.4876 0.56033 -0.15574 -0.11922 -0.052945 0.20112
-2.0607
Gradients: 0.32695 2.4407 0.16140 -1.6302 -2.7718 -1.1861
-1.7788 (norm 1.05e+000)
Iteration 9: loglikelihood = -136.495894655 (steplength = 1)
Parameters: 6.4896 0.58297 -0.15220 -0.11017 -0.066710 0.18134
-2.0469
Gradients: -0.43210 -0.65107 -0.17364 0.15633 0.59707 0.32961
0.36414 (norm 7.63e-001)
Iteration 10: loglikelihood = -136.490592511 (steplength = 1)
Parameters: 6.4886 0.57213 -0.15608 -0.11690 -0.061996 0.19671
-2.0648
Gradients: -0.097512 -0.22807 -0.23333 -0.23077 -0.058053 -0.28839
-0.074467 (norm 3.86e-001)
Iteration 11: loglikelihood = -136.490080201 (steplength = 1)
Parameters: 6.4884 0.56792 -0.15787 -0.11988 -0.060088 0.20265
-2.0736
Gradients: -0.026271 -0.042462 -0.11705 -0.17211 -0.13359 -0.25929
-0.11138 (norm 2.74e-001)
Iteration 12: loglikelihood = -136.489973117 (steplength = 1)
Parameters: 6.4883 0.56748 -0.15809 -0.12036 -0.059698 0.20303
-2.0754
Gradients: 0.014754 0.015626 -0.015933 -0.033397 -0.049127 -0.037086
-0.030232 (norm 1.62e-001)
Iteration 13: loglikelihood = -136.489964277 (steplength = 1)
Parameters: 6.4883 0.56727 -0.15829 -0.12056 -0.059753 0.20348
-2.0763
Gradients: -0.0068714 -0.0023991 6.6724e-006 0.00028924 0.0033536 -0.0024461
0.00092363 (norm 8.33e-002)
Iteration 14: loglikelihood = -136.489964105 (steplength = 1)
Parameters: 6.4883 0.56731 -0.15825 -0.12052 -0.059747 0.20339
-2.0762
Gradients: 0.0010810-8.4809e-005 1.7192e-005 0.00019304 0.00019005 0.00043713
0.00024676 (norm 3.32e-002)
Iteration 15: loglikelihood = -136.489964103 (steplength = 1)
Parameters: 6.4883 0.56731 -0.15825 -0.12053 -0.059747 0.20339
-2.0762
Gradients: -0.00012818 5.0844e-005 2.7890e-005 2.0559e-005-3.7774e-005 2.5363e-005
-3.0714e-005 (norm 1.16e-002)
Iteration 15: loglikelihood = -136.489964103 (steplength = 1)
Parameters: 6.4883 0.56731 -0.15826 -0.12053 -0.059747 0.20339
-2.0762
Gradients: -0.00012818 5.0844e-005 2.7890e-005 2.0559e-005-3.7774e-005 2.5363e-005
-3.0714e-005 (norm 1.16e-002)
--- FINAL VALUES:
loglikelihood = -136.489964103 (steplength = 5.12e-007)
Parameters: 6.4883 0.56731 -0.15826 -0.12053 -0.059747 0.20339
-2.0762
Gradients: -0.00012818 5.0844e-005 2.7890e-005 2.0559e-005-3.7774e-005 2.5363e-005
-3.0714e-005 (norm 1.16e-002)
Function evaluations: 47
Evaluations of gradient: 15
Model 1: ARMAX, using observations 1950:1-1998:2 (T = 194)
Estimated using AS 197 (exact ML)
Dependent variable: y
Standard errors based on Hessian
coefficient std. error z p-value
---------------------------------------------------------
const 6.48832 0.0467055 138.9 0.0000 ***
phi_1 0.567313 0.159434 3.558 0.0004 ***
phi_2 −0.158255 0.107503 −1.472 0.1410
phi_3 −0.120526 0.130267 −0.9252 0.3549
Phi_1 −0.0597470 0.121899 −0.4901 0.6240
y_one 0.203395 0.233933 0.8695 0.3846
y_two −2.07615 0.389196 −5.334 9.58e-08 ***
Mean dependent var 6.480000 S.D. dependent var 1.000000
Mean of innovations −0.001117 S.D. of innovations 0.488410
Log-likelihood −136.4900 Akaike criterion 288.9799
Schwarz criterion 315.1228 Hannan-Quinn 299.5659
Real Imaginary Modulus Frequency
-----------------------------------------------------------
AR
Root 1 1.0476 -1.1562 1.5602 -0.1328
Root 2 1.0476 1.1562 1.5602 0.1328
Root 3 -3.4083 0.0000 3.4083 0.5000
AR (seasonal)
Root 1 -16.7372 0.0000 16.7372 0.5000
-----------------------------------------------------------