Anomalies in a history

match flagged ← All logistic growth benchmarks

anomalies(history, { seed }) against fitting in Python, predicting the same history and comparing each value with its 99% range. 365 daily rows of a capped trend whose growth rate changes with three added outliers, which both libraries must flag.

Input

benchmark/inputs/v7/logistic-anomalies.json: 365 history rows and 0 forecast rows.

Output

Largest difference: 0.11 (0.073% of the input's range).

Every forecast row from both libraries.

Date	Effect Prophet	Python Prophet	Difference
2020-01-01	10.5120	10.6092	0.097
2020-01-02	11.0903	11.1882	0.098
2020-01-03	11.5359	11.6345	0.099
2020-01-04	11.4205	11.5197	0.099
2020-01-05	10.1740	10.2739	0.10
2020-01-06	9.3219	9.4223	0.10
2020-01-07	10.2175	10.3186	0.10
2020-01-08	11.6550	11.7551	0.10
2020-01-09	12.2499	12.3506	0.10
2020-01-10	12.7123	12.8136	0.10
2020-01-11	12.6139	12.7158	0.10
2020-01-12	11.3847	11.4871	0.10
2020-01-13	10.5501	10.6529	0.10
2020-01-14	11.4633	11.5667	0.10
2020-01-15	12.9188	13.0210	0.10
2020-01-16	13.5318	13.6346	0.10
2020-01-17	14.0125	14.1158	0.10
2020-01-18	13.9327	14.0364	0.10
2020-01-19	12.7223	12.8264	0.10
2020-01-20	11.9066	12.0111	0.10
2020-01-21	12.8391	12.9441	0.10
2020-01-22	14.3141	14.4177	0.10
2020-01-23	14.9468	15.0509	0.10
2020-01-24	15.4475	15.5519	0.10
2020-01-25	15.3878	15.4926	0.10
2020-01-26	14.1978	14.3028	0.11
2020-01-27	13.4028	13.5081	0.11
2020-01-28	14.3562	14.4617	0.11
2020-01-29	15.8523	15.9564	0.10
2020-01-30	16.5063	16.6107	0.10
2020-01-31	17.0286	17.1333	0.10
2020-02-01	16.9909	17.0956	0.10
2020-02-02	15.8229	15.9278	0.10
2020-02-03	15.0503	15.1552	0.10
2020-02-04	16.0263	16.1313	0.11
2020-02-05	17.5452	17.6486	0.10
2020-02-06	18.2224	18.3259	0.10
2020-02-07	18.7680	18.8716	0.10
2020-02-08	18.7538	18.8573	0.10
2020-02-09	17.6097	17.7132	0.10
2020-02-10	16.8612	16.9645	0.10
2020-02-11	17.8616	17.9647	0.10
2020-02-12	19.4051	19.5064	0.10
2020-02-13	20.1071	20.2083	0.10
2020-02-14	20.6778	20.7789	0.10
2020-02-15	20.6890	20.7898	0.10
2020-02-16	19.5705	19.6710	0.10
2020-02-17	18.8479	18.9480	0.10
2020-02-18	19.8743	19.9741	0.10
2020-02-19	21.4442	21.5419	0.098
2020-02-20	22.1728	22.2702	0.097
2020-02-21	22.7705	22.8674	0.097
2020-02-22	22.8088	22.9052	0.096
2020-02-23	21.7177	21.8135	0.096
2020-02-24	21.0227	21.1179	0.095
2020-02-25	22.0770	22.1716	0.095
2020-02-26	23.6750	23.7673	0.092
2020-02-27	24.4320	24.5237	0.092
2020-02-28	25.0583	25.1492	0.091
2020-02-29	25.1255	25.2156	0.090
2020-03-01	24.0636	24.1528	0.089
2020-03-02	23.3979	23.4862	0.088
2020-03-03	24.4819	24.5692	0.087
2020-03-04	26.1097	26.1945	0.085
2020-03-05	26.8969	26.9807	0.084
2020-03-06	27.5535	27.6362	0.083
2020-03-07	27.6512	27.7329	0.082
2020-03-08	26.6201	26.7005	0.080
2020-03-09	25.9855	26.0646	0.079
2020-03-10	27.1007	27.1786	0.078
2020-03-11	28.7601	28.8350	0.075
2020-03-12	29.5789	29.6526	0.074
2020-03-13	30.2675	30.3397	0.072
2020-03-14	30.3974	30.4682	0.071
2020-03-15	29.3986	29.4678	0.069
2020-03-16	28.7966	28.8642	0.068
2020-03-17	29.9447	30.0106	0.066
2020-03-18	31.6370	31.6996	0.063
2020-03-19	32.4891	32.5500	0.061
2020-03-20	33.2110	33.2702	0.059
2020-03-21	33.3746	33.4318	0.057
2020-03-22	32.4096	32.4649	0.055
2020-03-23	31.8415	31.8948	0.053
2020-03-24	33.0237	33.0750	0.051
2020-03-25	34.7504	34.7979	0.048
2020-03-26	35.6369	35.6824	0.045
2020-03-27	36.3936	36.4368	0.043
2020-03-28	36.5919	36.6329	0.041
2020-03-29	35.6619	35.7005	0.039
2020-03-30	35.1290	35.1651	0.036
2020-03-31	36.3464	36.3801	0.034
2020-04-01	38.1085	38.1381	0.030
2020-04-02	39.0306	39.0577	0.027
2020-04-03	39.8229	39.8473	0.024
2020-04-04	40.0570	40.0787	0.022
2020-04-05	39.1629	39.1818	0.019
2020-04-06	38.6659	38.6820	0.016
2020-04-07	39.9195	39.9326	0.013
2020-04-08	41.7177	41.7263	0.0086
2020-04-09	42.6761	42.6818	0.0057
2020-04-10	43.5047	43.5073	0.0026
2020-04-11	43.7752	43.7747	0.00051
2020-04-12	42.9175	42.9138	0.0037
2020-04-13	42.4571	42.4501	0.0071
2020-04-14	43.7472	43.7369	0.010
2020-04-15	45.5821	45.5667	0.015
2020-04-16	46.5466	46.5270	0.020
2020-04-17	47.3808	47.3569	0.024
2020-04-18	47.6564	47.6280	0.028
2020-04-19	46.8033	46.7703	0.033
2020-04-20	46.3469	46.3093	0.038
2020-04-21	47.6404	47.5982	0.042
2020-04-22	49.4782	49.4296	0.049
2020-04-23	50.4755	50.4221	0.053
2020-04-24	51.3425	51.2843	0.058
2020-04-25	51.6509	51.5877	0.063
2020-04-26	50.8305	50.7622	0.068
2020-04-27	50.2887	50.2173	0.071
2020-04-28	51.4951	51.4207	0.074
2020-04-29	53.2441	53.1649	0.079
2020-04-30	54.1508	54.0687	0.082
2020-05-01	54.9256	54.8404	0.085
2020-05-02	55.1401	55.0516	0.088
2020-05-03	54.2240	54.1323	0.092
2020-05-04	53.7029	53.6080	0.095
2020-05-05	54.9301	54.8318	0.098
2020-05-06	56.6996	56.5964	0.10
2020-05-07	57.6269	57.5205	0.11
2020-05-08	58.4222	58.3124	0.11
2020-05-09	58.4788	58.3699	0.11
2020-05-10	57.4032	57.2952	0.11
2020-05-11	56.7209	56.6138	0.11
2020-05-12	57.7851	57.6789	0.11
2020-05-13	59.3901	59.2832	0.11
2020-05-14	60.1511	60.0453	0.11
2020-05-15	60.7784	60.6736	0.10
2020-05-16	60.8436	60.7397	0.10
2020-05-17	59.7766	59.6737	0.10
2020-05-18	59.1029	59.0008	0.10
2020-05-19	60.1756	60.0746	0.10
2020-05-20	61.7890	61.6874	0.10
2020-05-21	62.4299	62.3315	0.098
2020-05-22	62.9363	62.8411	0.095
2020-05-23	62.8799	62.7878	0.092
2020-05-24	61.6905	61.6016	0.089
2020-05-25	60.8937	60.8078	0.086
2020-05-26	61.8426	61.7600	0.083
2020-05-27	63.3315	63.2505	0.081
2020-05-28	63.9757	63.8980	0.078
2020-05-29	64.4855	64.4111	0.074
2020-05-30	64.4325	64.3613	0.071
2020-05-31	63.2465	63.1786	0.068
2020-06-01	62.4328	62.3661	0.067
2020-06-02	63.3647	63.2993	0.065
2020-06-03	64.8366	64.7708	0.066
2020-06-04	65.4637	65.3993	0.064
2020-06-05	65.9563	65.8932	0.063
2020-06-06	65.8860	65.8241	0.062
2020-06-07	64.6826	64.6220	0.061
2020-06-08	63.8717	63.8123	0.059
2020-06-09	64.8064	64.7483	0.058
2020-06-10	66.2810	66.2226	0.058
2020-06-11	66.9109	66.8539	0.057
2020-06-12	67.4063	67.3506	0.056
2020-06-13	67.3387	67.2842	0.054
2020-06-14	66.1380	66.0849	0.053
2020-06-15	65.3298	65.2780	0.052
2020-06-16	66.2673	66.2168	0.051
2020-06-17	67.7446	67.6938	0.051
2020-06-18	68.3773	68.3279	0.049
2020-06-19	68.8753	68.8273	0.048
2020-06-20	68.8104	68.7637	0.047
2020-06-21	67.6125	67.5671	0.045
2020-06-22	66.8070	66.7629	0.044
2020-06-23	67.7471	67.7044	0.043
2020-06-24	69.2272	69.1842	0.043
2020-06-25	69.8625	69.8209	0.042
2020-06-26	70.3632	70.3230	0.040
2020-06-27	70.3010	70.2622	0.039
2020-06-28	69.1057	69.0683	0.037
2020-06-29	68.3029	68.2667	0.036
2020-06-30	69.2456	69.2109	0.035
2020-07-01	70.7283	70.6933	0.035
2020-07-02	71.3662	71.3327	0.033
2020-07-03	71.8696	71.8375	0.032
2020-07-04	71.8100	71.7793	0.031
2020-07-05	70.6173	70.5880	0.029
2020-07-06	69.8171	69.7891	0.028
2020-07-07	70.7624	70.7359	0.027
2020-07-08	72.2477	72.2210	0.027
2020-07-09	72.8882	72.8630	0.025
2020-07-10	73.3941	73.3703	0.024
2020-07-11	73.3371	73.3147	0.022
2020-07-12	72.1470	72.1260	0.021
2020-07-13	71.3493	71.3297	0.020
2020-07-14	72.2972	72.2790	0.018
2020-07-15	73.7850	73.7667	0.018
2020-07-16	74.4280	74.4112	0.017
2020-07-17	74.9364	74.9211	0.015
2020-07-18	74.8819	74.8680	0.014
2020-07-19	73.6943	73.6819	0.012
2020-07-20	72.8991	72.8881	0.011
2020-07-21	73.8495	73.8399	0.0095
2020-07-22	75.3398	75.3300	0.0097
2020-07-23	75.9852	75.9771	0.0081
2020-07-24	76.4961	76.4895	0.0066
2020-07-25	76.4441	76.4389	0.0052
2020-07-26	75.2589	75.2552	0.0037
2020-07-27	74.4661	74.4638	0.0023
2020-07-28	75.4189	75.4182	0.00078
2020-07-29	76.9116	76.9107	0.00092
2020-07-30	77.5595	77.5602	0.00071
2020-07-31	78.0728	78.0751	0.0023
2020-08-01	78.0231	78.0269	0.0038
2020-08-02	76.8404	76.8457	0.0053
2020-08-03	76.0500	76.0567	0.0068
2020-08-04	77.0052	77.0135	0.0083
2020-08-05	78.5002	78.5085	0.0082
2020-08-06	79.1505	79.1604	0.0099
2020-08-07	79.6661	79.6776	0.011
2020-08-08	79.6187	79.6317	0.013
2020-08-09	78.4383	78.4528	0.015
2020-08-10	77.7204	77.7371	0.017
2020-08-11	78.7484	78.7672	0.019
2020-08-12	80.3164	80.3358	0.019
2020-08-13	81.0398	81.0615	0.022
2020-08-14	81.6288	81.6527	0.024
2020-08-15	81.6549	81.6810	0.026
2020-08-16	80.5482	80.5764	0.028
2020-08-17	79.8340	79.8644	0.030
2020-08-18	80.8655	80.8982	0.033
2020-08-19	82.4371	82.4704	0.033
2020-08-20	83.1641	83.1996	0.036
2020-08-21	83.7566	83.7944	0.038
2020-08-22	83.9027	83.9406	0.038
2020-08-23	82.9162	82.9542	0.038
2020-08-24	82.3226	82.3607	0.038
2020-08-25	83.4752	83.5134	0.038
2020-08-26	85.1681	85.2048	0.037
2020-08-27	86.0167	86.0537	0.037
2020-08-28	86.7312	86.7684	0.037
2020-08-29	86.8832	86.9205	0.037
2020-08-30	85.9026	85.9400	0.037
2020-08-31	85.3149	85.3523	0.037
2020-09-01	86.4731	86.5107	0.038
2020-09-02	88.2978	88.3324	0.035
2020-09-03	89.2785	89.3119	0.033
2020-09-04	90.1255	90.1575	0.032
2020-09-05	90.4103	90.4410	0.031
2020-09-06	89.5629	89.5921	0.029
2020-09-07	89.1085	89.1364	0.028
2020-09-08	90.4006	90.4270	0.026
2020-09-09	92.2332	92.2566	0.023
2020-09-10	93.2217	93.2438	0.022
2020-09-11	94.0762	94.0970	0.021
2020-09-12	94.3684	94.3878	0.019
2020-09-13	93.5282	93.5461	0.018
2020-09-14	93.1064	93.1243	0.018
2020-09-15	94.4308	94.4488	0.018
2020-09-16	96.2957	96.3121	0.016
2020-09-17	97.3164	97.3330	0.017
2020-09-18	98.2029	98.2196	0.017
2020-09-19	98.5270	98.5437	0.017
2020-09-20	97.7185	97.7352	0.017
2020-09-21	97.3027	97.3195	0.017
2020-09-22	98.6329	98.6498	0.017
2020-09-23	100.5034	100.5186	0.015
2020-09-24	101.5294	101.5448	0.015
2020-09-25	102.4210	102.4365	0.015
2020-09-26	102.7499	102.7655	0.016
2020-09-27	101.9460	101.9616	0.016
2020-09-28	101.5346	101.5502	0.016
2020-09-29	102.8690	102.8846	0.016
2020-09-30	104.7434	104.7574	0.014
2020-10-01	105.7730	105.7872	0.014
2020-10-02	106.6681	106.6823	0.014
2020-10-03	107.0002	107.0145	0.014
2020-10-04	106.1992	106.2135	0.014
2020-10-05	105.7905	105.8048	0.014
2020-10-06	107.1274	107.1417	0.014
2020-10-07	109.0039	109.0166	0.013
2020-10-08	110.0356	110.0484	0.013
2020-10-09	110.9324	110.9453	0.013
2020-10-10	111.2659	111.2789	0.013
2020-10-11	110.4662	110.4791	0.013
2020-10-12	110.0585	110.0714	0.013
2020-10-13	111.3961	111.4090	0.013
2020-10-14	113.2731	113.2845	0.011
2020-10-15	114.3050	114.3165	0.011
2020-10-16	115.2018	115.2134	0.012
2020-10-17	115.5352	115.5467	0.012
2020-10-18	114.7350	114.7465	0.012
2020-10-19	114.3266	114.3381	0.012
2020-10-20	115.6632	115.6747	0.012
2020-10-21	117.5390	117.5490	0.010
2020-10-22	118.5695	118.5796	0.010
2020-10-23	119.4646	119.4747	0.010
2020-10-24	119.7960	119.8062	0.010
2020-10-25	118.9937	119.0038	0.010
2020-10-26	118.5828	118.5930	0.010
2020-10-27	119.9168	119.9270	0.010
2020-10-28	121.7898	121.7984	0.0086
2020-10-29	122.8171	122.8258	0.0087
2020-10-30	123.7089	123.7176	0.0087
2020-10-31	124.0368	124.0455	0.0087
2020-11-01	123.2306	123.2393	0.0087
2020-11-02	122.8157	122.8244	0.0087
2020-11-03	124.1454	124.1542	0.0088
2020-11-04	126.0139	126.0210	0.0072
2020-11-05	127.0364	127.0437	0.0073
2020-11-06	127.9233	127.9306	0.0073
2020-11-07	128.2459	128.2533	0.0073
2020-11-08	127.4343	127.4416	0.0073
2020-11-09	127.0138	127.0211	0.0073
2020-11-10	128.3376	128.3450	0.0074
2020-11-11	130.2000	130.2058	0.0058
2020-11-12	131.2163	131.2222	0.0059
2020-11-13	132.0966	132.1025	0.0059
2020-11-14	132.4125	132.4185	0.0060
2020-11-15	131.5940	131.5999	0.0059
2020-11-16	131.1663	131.1722	0.0059
2020-11-17	132.4828	132.4887	0.0060
2020-11-18	134.3376	134.3420	0.0044
2020-11-19	135.3461	135.3506	0.0045
2020-11-20	136.2184	136.2230	0.0046
2020-11-21	136.5261	136.5307	0.0046
2020-11-22	135.6992	135.7038	0.0046
2020-11-23	135.2629	135.2675	0.0046
2020-11-24	136.5706	136.5752	0.0046
2020-11-25	138.4165	138.4195	0.0030
2020-11-26	139.4158	139.4189	0.0032
2020-11-27	140.2787	140.2820	0.0032
2020-11-28	140.5769	140.5802	0.0033
2020-11-29	139.7402	139.7435	0.0033
2020-11-30	139.2941	139.2973	0.0033
2020-12-01	140.5917	140.5950	0.0033
2020-12-02	142.4272	142.4290	0.0017
2020-12-03	143.4161	143.4180	0.0019
2020-12-04	144.2685	144.2704	0.0019
2020-12-05	144.5559	144.5578	0.0020
2020-12-06	143.7082	143.7102	0.0020
2020-12-07	143.2509	143.2529	0.0020
2020-12-08	144.5372	144.5393	0.0021
2020-12-09	146.3614	146.3618	0.00047
2020-12-10	147.3386	147.3392	0.00062
2020-12-11	148.1792	148.1799	0.00070
2020-12-12	148.4547	148.4554	0.00073
2020-12-13	147.5949	147.5957	0.00075
2020-12-14	147.1254	147.1262	0.00076
2020-12-15	148.3994	148.4002	0.00085
2020-12-16	150.2110	150.2102	0.00073
2020-12-17	151.1756	151.1750	0.00057
2020-12-18	152.0034	152.0029	0.00049
2020-12-19	152.2659	152.2655	0.00044
2020-12-20	151.3931	151.3927	0.00041
2020-12-21	150.9104	150.9101	0.00039
2020-12-22	152.1711	152.1708	0.00030
2020-12-23	153.9692	153.9674	0.0019
2020-12-24	154.9203	154.9186	0.0017
2020-12-25	155.7344	155.7328	0.0016
2020-12-26	155.9831	155.9816	0.0016
2020-12-27	155.0964	155.0949	0.0015
2020-12-28	154.5997	154.5982	0.0015
2020-12-29	155.8462	155.8448	0.0014
2020-12-30	157.6301	157.6272	0.0029

Internal fit differences

The forecasts match, so this case passes. Both libraries search for the best-fitting parameters and stop when they are close enough. On this input they stopped at slightly different points, so these internal numbers differ by more than the threshold where we take a closer look.

Check	Effect Prophet	Python Prophet	Threshold
Fitting objective (lower is a better fit)	-1234.5954	-1233.9977	0.01

Timing

Median of all measured repetitions.

Step	Effect Prophet	Python Prophet	Effect Prophet is
Fit	51.9 ms	45.1 ms	1.2× slower
Simulate uncertainty	14.5 ms	251 ms	Not compared: different work
Fit and find anomalies	71.6 ms	298 ms	4.2× faster

Some steps aren't compared, because the two libraries' public calls produce different outputs. Their times show what each call costs, not which library is faster.

• Simulate uncertainty: Python's predict(vectorized=False) also builds the point forecast and every component, while Effect Prophet's predictUncertainty returns only the ranges.

Settings

The case declaration both libraries ran.

{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "logistic-python-reconciliation-v1"
  },
  "fitRequest": "growth-only",
  "configuration": {
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    ],
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  "pythonOptimizer": {
    "algorithm": "Auto",
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  "uncertainty": {
    "seed": 19,
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    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
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  "anomalies": {
    "expected": [
      "2020-03-11T00:00:00.000Z",
      "2020-06-29T00:00:00.000Z",
      "2020-10-17T00:00:00.000Z"
    ]
  }
}