Regressors that track other effects

match ← All flat growth benchmarks

Two years of daily rows. Temperature follows the yearly pattern closely and a constant regressor duplicates the level. The forecast half-year has an unusually warm winter, so the split between temperature and the yearly pattern shows.

Input

benchmark/inputs/v4/flat-correlated-regressors.json: 730 history rows and 180 forecast rows.

Output

Largest difference: 2.8e-11 (< 0.0001% of the input's range).

Every forecast row from both libraries.

Date	Effect Prophet	Python Prophet	Difference
2021-12-31	49.0310	49.0310	2.1e-11
2022-01-01	47.9048	47.9048	2.2e-11
2022-01-02	47.1011	47.1011	2.3e-11
2022-01-03	47.2331	47.2331	2.3e-11
2022-01-04	48.1731	48.1731	2.1e-11
2022-01-05	49.2510	49.2510	2.0e-11
2022-01-06	49.7018	49.7018	2.0e-11
2022-01-07	49.1683	49.1683	2.1e-11
2022-01-08	48.0608	48.0608	2.2e-11
2022-01-09	47.2788	47.2788	2.3e-11
2022-01-10	47.4255	47.4255	2.3e-11
2022-01-11	48.3689	48.3689	2.1e-11
2022-01-12	49.4429	49.4429	2.0e-11
2022-01-13	49.8921	49.8921	2.0e-11
2022-01-14	49.3673	49.3673	2.1e-11
2022-01-15	48.2789	48.2789	2.2e-11
2022-01-16	47.5186	47.5186	2.3e-11
2022-01-17	47.6801	47.6801	2.2e-11
2022-01-18	48.6266	48.6266	2.1e-11
2022-01-19	49.6965	49.6965	2.0e-11
2022-01-20	50.1441	50.1441	2.0e-11
2022-01-21	49.6279	49.6279	2.1e-11
2022-01-22	48.5582	48.5582	2.2e-11
2022-01-23	47.8191	47.8191	2.3e-11
2022-01-24	47.9944	47.9944	2.3e-11
2022-01-25	48.9432	48.9432	2.1e-11
2022-01-26	50.0081	50.0081	2.0e-11
2022-01-27	50.4532	50.4532	2.0e-11
2022-01-28	49.9447	49.9447	2.1e-11
2022-01-29	48.8929	48.8929	2.2e-11
2022-01-30	48.1737	48.1737	2.3e-11
2022-01-31	48.3614	48.3614	2.3e-11
2022-02-01	49.3111	49.3111	2.2e-11
2022-02-02	50.3697	50.3697	2.1e-11
2022-02-03	50.8112	50.8112	2.1e-11
2022-02-04	50.3094	50.3094	2.2e-11
2022-02-05	49.2743	49.2743	2.3e-11
2022-02-06	48.5738	48.5738	2.4e-11
2022-02-07	48.7727	48.7727	2.3e-11
2022-02-08	49.7218	49.7218	2.2e-11
2022-02-09	50.7731	50.7731	2.1e-11
2022-02-10	51.2102	51.2102	2.1e-11
2022-02-11	50.7146	50.7146	2.2e-11
2022-02-12	49.6955	49.6955	2.3e-11
2022-02-13	49.0130	49.0130	2.4e-11
2022-02-14	49.2221	49.2221	2.4e-11
2022-02-15	50.1699	50.1699	2.3e-11
2022-02-16	51.2132	51.2132	2.1e-11
2022-02-17	51.6456	51.6456	2.1e-11
2022-02-18	51.1557	51.1557	2.2e-11
2022-02-19	50.1523	50.1523	2.4e-11
2022-02-20	49.4871	49.4871	2.4e-11
2022-02-21	49.7056	49.7056	2.4e-11
2022-02-22	50.6514	50.6514	2.3e-11
2022-02-23	51.6862	51.6862	2.2e-11
2022-02-24	52.1132	52.1132	2.1e-11
2022-02-25	51.6286	51.6286	2.2e-11
2022-02-26	50.6403	50.6403	2.4e-11
2022-02-27	49.9915	49.9915	2.4e-11
2022-02-28	50.2185	50.2185	2.4e-11
2022-03-01	51.1611	51.1611	2.3e-11
2022-03-02	52.1862	52.1862	2.2e-11
2022-03-03	52.6071	52.6071	2.2e-11
2022-03-04	52.1268	52.1268	2.3e-11
2022-03-05	51.1524	51.1524	2.4e-11
2022-03-06	50.5188	50.5188	2.5e-11
2022-03-07	50.7526	50.7526	2.5e-11
2022-03-08	51.6906	51.6906	2.3e-11
2022-03-09	52.7047	52.7047	2.2e-11
2022-03-10	53.1181	53.1181	2.2e-11
2022-03-11	52.6412	52.6412	2.3e-11
2022-03-12	51.6794	51.6794	2.5e-11
2022-03-13	51.0596	51.0596	2.5e-11
2022-03-14	51.2987	51.2987	2.5e-11
2022-03-15	52.2304	52.2304	2.4e-11
2022-03-16	53.2322	53.2322	2.3e-11
2022-03-17	53.6372	53.6372	2.3e-11
2022-03-18	53.1625	53.1625	2.4e-11
2022-03-19	52.2124	52.2124	2.5e-11
2022-03-20	51.6051	51.6051	2.6e-11
2022-03-21	51.8483	51.8483	2.5e-11
2022-03-22	52.7727	52.7727	2.4e-11
2022-03-23	53.7612	53.7612	2.3e-11
2022-03-24	54.1569	54.1569	2.3e-11
2022-03-25	53.6837	53.6837	2.4e-11
2022-03-26	52.7445	52.7445	2.5e-11
2022-03-27	52.1488	52.1488	2.6e-11
2022-03-28	52.3950	52.3950	2.6e-11
2022-03-29	53.3109	53.3109	2.4e-11
2022-03-30	54.2852	54.2852	2.3e-11
2022-03-31	54.6709	54.6709	2.3e-11
2022-04-01	54.1986	54.1986	2.4e-11
2022-04-02	53.2696	53.2696	2.5e-11
2022-04-03	52.6843	52.6843	2.6e-11
2022-04-04	52.9324	52.9324	2.6e-11
2022-04-05	53.8386	53.8386	2.5e-11
2022-04-06	54.7977	54.7977	2.4e-11
2022-04-07	55.1725	55.1725	2.3e-11
2022-04-08	54.7002	54.7002	2.4e-11
2022-04-09	53.7801	53.7801	2.6e-11
2022-04-10	53.2042	53.2042	2.6e-11
2022-04-11	53.4526	53.4526	2.6e-11
2022-04-12	54.3478	54.3478	2.5e-11
2022-04-13	55.2903	55.2903	2.4e-11
2022-04-14	55.6532	55.6532	2.4e-11
2022-04-15	55.1798	55.1798	2.5e-11
2022-04-16	54.2676	54.2676	2.6e-11
2022-04-17	53.6996	53.6996	2.7e-11
2022-04-18	53.9469	53.9469	2.6e-11
2022-04-19	54.8297	54.8297	2.5e-11
2022-04-20	55.7546	55.7546	2.4e-11
2022-04-21	56.1045	56.1045	2.4e-11
2022-04-22	55.6292	55.6292	2.5e-11
2022-04-23	54.7239	54.7239	2.6e-11
2022-04-24	54.1627	54.1627	2.7e-11
2022-04-25	54.4079	54.4079	2.7e-11
2022-04-26	55.2771	55.2771	2.6e-11
2022-04-27	56.1835	56.1835	2.4e-11
2022-04-28	56.5198	56.5198	2.4e-11
2022-04-29	56.0420	56.0420	2.5e-11
2022-04-30	55.1430	55.1430	2.6e-11
2022-05-01	54.5878	54.5878	2.7e-11
2022-05-02	54.8298	54.8298	2.7e-11
2022-05-03	55.6848	55.6848	2.6e-11
2022-05-04	56.5719	56.5719	2.5e-11
2022-05-05	56.8941	56.8941	2.4e-11
2022-05-06	56.4133	56.4133	2.5e-11
2022-05-07	55.5201	55.5201	2.7e-11
2022-05-08	54.9701	54.9701	2.7e-11
2022-05-09	55.2081	55.2081	2.7e-11
2022-05-10	56.0477	56.0477	2.6e-11
2022-05-11	56.9150	56.9150	2.5e-11
2022-05-12	57.2225	57.2225	2.4e-11
2022-05-13	56.7382	56.7382	2.5e-11
2022-05-14	55.8499	55.8499	2.7e-11
2022-05-15	55.3043	55.3043	2.7e-11
2022-05-16	55.5371	55.5371	2.7e-11
2022-05-17	56.3605	56.3605	2.6e-11
2022-05-18	57.2070	57.2070	2.5e-11
2022-05-19	57.4991	57.4991	2.5e-11
2022-05-20	57.0107	57.0107	2.6e-11
2022-05-21	56.1267	56.1267	2.7e-11
2022-05-22	55.5845	55.5845	2.8e-11
2022-05-23	55.8112	55.8112	2.7e-11
2022-05-24	56.6175	56.6175	2.6e-11
2022-05-25	57.4424	57.4424	2.5e-11
2022-05-26	57.7188	57.7188	2.5e-11
2022-05-27	57.2258	57.2258	2.6e-11
2022-05-28	56.3456	56.3456	2.7e-11
2022-05-29	55.8061	55.8061	2.8e-11
2022-05-30	56.0261	56.0261	2.7e-11
2022-05-31	56.8146	56.8146	2.6e-11
2022-06-01	57.6178	57.6178	2.5e-11
2022-06-02	57.8782	57.8782	2.5e-11
2022-06-03	57.3806	57.3806	2.6e-11
2022-06-04	56.5039	56.5039	2.7e-11
2022-06-05	55.9669	55.9669	2.8e-11
2022-06-06	56.1796	56.1796	2.7e-11
2022-06-07	56.9501	56.9501	2.6e-11
2022-06-08	57.7313	57.7313	2.5e-11
2022-06-09	57.9758	57.9758	2.5e-11
2022-06-10	57.4736	57.4736	2.6e-11
2022-06-11	56.6004	56.6004	2.7e-11
2022-06-12	56.0656	56.0656	2.8e-11
2022-06-13	56.2708	56.2708	2.7e-11
2022-06-14	57.0229	57.0229	2.6e-11
2022-06-15	57.7820	57.7820	2.5e-11
2022-06-16	58.0106	58.0106	2.5e-11
2022-06-17	57.5039	57.5039	2.6e-11
2022-06-18	56.6341	56.6341	2.7e-11
2022-06-19	56.1011	56.1011	2.8e-11
2022-06-20	56.2983	56.2983	2.7e-11
2022-06-21	57.0317	57.0317	2.6e-11
2022-06-22	57.7685	57.7685	2.5e-11
2022-06-23	57.9812	57.9812	2.5e-11
2022-06-24	57.4699	57.4699	2.6e-11
2022-06-25	56.6035	56.6035	2.7e-11
2022-06-26	56.0721	56.0721	2.7e-11
2022-06-27	56.2610	56.2610	2.7e-11
2022-06-28	56.9753	56.9753	2.6e-11

Timing

Median of all measured repetitions.

Step	Effect Prophet	Python Prophet	Effect Prophet is
Convert input rows	101 µs	932 µs	9.2× faster
Fit	5.10 ms	25.4 ms	5.0× faster
Predict	924 µs	4.55 ms	4.9× faster
Fit and predict	5.42 ms	29.6 ms	5.5× faster
Convert, fit and predict	6.99 ms	30.4 ms	4.4× faster
First forecast in a new process	183 ms	1.45 s	7.9× faster
Save model to JSON	26 µs	1.15 ms	44× faster
Load model from JSON	202 µs	3.54 ms	17× faster
Load and predict in a new process	196 ms	1.40 s	7.1× faster

Settings

The case declaration both libraries ran.

{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "flat-map-additive-v1"
  },
  "configuration": {
    "growth": "flat",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "auto",
      "count": 25,
      "range": 0.8
    },
    "changepointPriorScale": 0.05,
    "seasonalities": [
      {
        "name": "yearly-custom",
        "periodDays": 365.25,
        "fourierOrder": 10,
        "priorScale": 10
      },
      {
        "name": "weekly-custom",
        "periodDays": 7,
        "fourierOrder": 2,
        "priorScale": 10
      }
    ],
    "events": [],
    "regressors": [
      {
        "name": "temperature",
        "priorScale": 10,
        "standardization": "auto"
      },
      {
        "name": "baseline",
        "priorScale": 10,
        "standardization": "never"
      }
    ]
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  }
}