On Windows, I used OpenAI Codex CLI to generate the code here, using the instructions in prompt.txt. The Approval Mode was Full Access.
The code was required to run with gfortran and ifx with debugging options and to pass fortitude check.
The code is commented so that documentation can be created using FORD. Codex took about 15 minutes to create a working program. Here is sample truncated output.
AR Monte Carlo experiment configuration:
Number of observations: 1000
Number of simulations: 10
Maximum AR order fitted: 6
Maximum ACF lag compared: 20
True AR coefficients: 0.100 0.100 -0.100
Innovation standard deviation: 1.000
Normal RNG diagnostics:
Mean: 0.000444
Variance: 1.001254
Kurtosis: 2.991856
Empirical versus theoretical ACF (first simulation):
Lag 0 : empirical = 1.000000, theoretical = 1.000000
Lag 1 : empirical = 0.118298, theoretical = 0.100000
Lag 2 : empirical = 0.127890, theoretical = 0.100000
Lag 3 : empirical = -0.011970, theoretical = -0.080000
Lag 4 : empirical = 0.024423, theoretical = -0.008000
Lag 5 : empirical = -0.038231, theoretical = -0.018800
Lag 6 : empirical = 0.005852, theoretical = 0.005320
Lag 7 : empirical = -0.018721, theoretical = -0.000548
Lag 8 : empirical = -0.007431, theoretical = 0.002357
Lag 9 : empirical = 0.022611, theoretical = -0.000351
Lag 10 : empirical = -0.010081, theoretical = 0.000255
Maximum absolute difference across lags: 0.068030
Simulation 1
AR order: 0
AR(0) model (white noise)
Innovation variance: 1.011054
AICC: 10.993043
BIC: 10.993043
AR order: 1
True coefficients: 0.100000
Estimated coefficients: 0.118298
Innovation variance: 0.996904
AICC: -1.096326
BIC: 3.807421
AR order: 2
True coefficients: 0.100000 0.100000
Estimated coefficients: 0.104634 0.115512
Innovation variance: 0.983603
AICC: -12.521209
BIC: -2.717735
AR order: 3
True coefficients: 0.100000 0.100000 -0.100000
Estimated coefficients: 0.109266 0.119709 -0.040106
Innovation variance: 0.982021
AICC: -12.118906
BIC: 2.580263
AR order: 4
True coefficients: 0.100000 0.100000 -0.100000 0.000000
Estimated coefficients: 0.109892 0.117840 -0.041812 0.015614
Innovation variance: 0.981781
AICC: -10.346636
BIC: 9.244184
AR order: 5
True coefficients: 0.100000 0.100000 -0.100000 0.000000 0.000000
Estimated coefficients: 0.110471 0.116289 -0.037442 0.019689 -0.037078
Innovation variance: 0.980431
AICC: -9.702207
BIC: 14.776207
AR order: 6
True coefficients: 0.100000 0.100000 -0.100000 0.000000 0.000000 0.000000
Estimated coefficients: 0.110802 0.116113 -0.037108 0.018651 -0.038064 0.008926
Innovation variance: 0.980353
AICC: -7.757650
BIC: 21.604290
Best order by AICC: 2
Best order by BIC : 2
<snip>
Selection summary over simulations:
Order 0: AICC chosen 0 times, BIC chosen 0 times
Order 1: AICC chosen 0 times, BIC chosen 3 times
Order 2: AICC chosen 1 times, BIC chosen 3 times
Order 3: AICC chosen 8 times, BIC chosen 4 times
Order 4: AICC chosen 0 times, BIC chosen 0 times
Order 5: AICC chosen 0 times, BIC chosen 0 times
Order 6: AICC chosen 1 times, BIC chosen 0 times
Total CPU time (seconds): 0.0156