Fractional-memory recurrent state / results.json

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  1{
  2  "prediction_stability_half_life": [
  3    {
  4      "rho": 0.8,
  5      "predicted_half_life": 3.1062837195053903,
  6      "observed_half_life": 4,
  7      "max_impulse": 0.19999999999999996,
  8      "stable_max_state": 0.9999999999999994
  9    },
 10    {
 11      "rho": 0.95,
 12      "predicted_half_life": 13.513407333964874,
 13      "observed_half_life": 14,
 14      "max_impulse": 0.050000000000000044,
 15      "stable_max_state": 1.0
 16    },
 17    {
 18      "rho": 0.99,
 19      "predicted_half_life": 68.96756393652842,
 20      "observed_half_life": 69,
 21      "max_impulse": 0.010000000000000009,
 22      "stable_max_state": 0.9999999999999979
 23    },
 24    {
 25      "rho": 0.999,
 26      "predicted_half_life": 692.8005491785002,
 27      "observed_half_life": 693,
 28      "max_impulse": 0.0010000000000000009,
 29      "stable_max_state": 0.9999999979593749
 30    }
 31  ],
 32  "prediction_powerlaw": [
 33    {
 34      "lag": 100,
 35      "observed": 0.5614099274382258,
 36      "predicted": 0.5641895835477563,
 37      "relative_error": 0.004926812175530308
 38    },
 39    {
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 41      "observed": 0.5639079108440004,
 42      "predicted": 0.5641895835477563,
 43      "relative_error": 0.0004992518684671091
 44    },
 45    {
 46      "lag": 10000,
 47      "observed": 0.5641613782989433,
 48      "predicted": 0.5641895835477563,
 49      "relative_error": 4.9992501874303284e-05
 50    },
 51    {
 52      "lag": 100000,
 53      "observed": 0.5641867626421517,
 54      "predicted": 0.5641895835477563,
 55      "relative_error": 4.9999250018261025e-06
 56    },
 57    {
 58      "lag": 1000000,
 59      "observed": 0.5641893014533876,
 60      "predicted": 0.5641895835477563,
 61      "relative_error": 4.999992500184989e-07
 62    }
 63  ],
 64  "prediction_bank_scaling": [
 65    {
 66      "K": 1,
 67      "relative_fit_error": 101.98936827263357
 68    },
 69    {
 70      "K": 2,
 71      "relative_fit_error": 0.8180064042638799
 72    },
 73    {
 74      "K": 4,
 75      "relative_fit_error": 0.33798994885993666
 76    },
 77    {
 78      "K": 8,
 79      "relative_fit_error": 0.31358247352246277
 80    },
 81    {
 82      "K": 16,
 83      "relative_fit_error": 0.31270798561092067
 84    },
 85    {
 86      "K": 32,
 87      "relative_fit_error": 0.31291395381295295
 88    }
 89  ],
 90  "secondary_filter_comparison": {
 91    "fractional_K8_mse": 0.0006432590283113826,
 92    "best_single_exponential_mse": 0.00012002695213538339,
 93    "single_over_fractional": 0.18659194329610232
 94  },
 95  "secondary_delayed_impulse": {
 96    "delay": 4000,
 97    "fractional_at_delay": 1.5167383864969127e-05,
 98    "single_at_delay": 1.2912823376253832e-58,
 99    "ratio": 1.1745985694237359e+53
100  }
101}