Anomalies in a history

match flagged ← All linear 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 bending trend with four added outliers, which both libraries must flag.

Input

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

Output

Largest difference: 0.15 (0.11% of the input's range).

Every forecast row from both libraries.

Date	Effect Prophet	Python Prophet	Difference
2020-01-01	12.0042	11.9825	0.022
2020-01-02	13.5386	13.5183	0.020
2020-01-03	14.3027	14.2843	0.018
2020-01-04	13.9155	13.8988	0.017
2020-01-05	13.0784	13.0634	0.015
2020-01-06	12.8188	12.8047	0.014
2020-01-07	13.5418	13.5287	0.013
2020-01-08	14.9849	14.9738	0.011
2020-01-09	16.5193	16.5096	0.0097
2020-01-10	17.2833	17.2756	0.0078
2020-01-11	16.8962	16.8900	0.0061
2020-01-12	16.0591	16.0547	0.0044
2020-01-13	15.7995	15.7960	0.0035
2020-01-14	16.5224	16.5199	0.0025
2020-01-15	17.9655	17.9651	0.00045
2020-01-16	19.4999	19.5009	0.00096
2020-01-17	20.2640	20.2669	0.0029
2020-01-18	19.8768	19.8813	0.0045
2020-01-19	19.0398	19.0459	0.0062
2020-01-20	18.7801	18.7873	0.0071
2020-01-21	19.5031	19.5112	0.0081
2020-01-22	20.9462	20.9563	0.010
2020-01-23	22.4806	22.4922	0.012
2020-01-24	23.2447	23.2581	0.013
2020-01-25	22.8575	22.8726	0.015
2020-01-26	22.0204	22.0372	0.017
2020-01-27	21.7608	21.7785	0.018
2020-01-28	22.4838	22.5025	0.019
2020-01-29	23.9268	23.9476	0.021
2020-01-30	25.4612	25.4834	0.022
2020-01-31	26.2253	26.2494	0.024
2020-02-01	25.8381	25.8639	0.026
2020-02-02	25.0011	25.0285	0.027
2020-02-03	24.7415	24.7698	0.028
2020-02-04	25.4644	25.4938	0.029
2020-02-05	26.9075	26.9389	0.031
2020-02-06	28.4419	28.4747	0.033
2020-02-07	29.2060	29.2407	0.035
2020-02-08	28.8188	28.8552	0.036
2020-02-09	27.9817	28.0198	0.038
2020-02-10	27.7221	27.7611	0.039
2020-02-11	28.4451	28.4850	0.040
2020-02-12	29.8882	29.9302	0.042
2020-02-13	31.4226	31.4660	0.043
2020-02-14	32.1866	32.2320	0.045
2020-02-15	31.7995	31.8464	0.047
2020-02-16	30.9624	31.0111	0.049
2020-02-17	30.7028	30.7524	0.050
2020-02-18	31.4166	31.4613	0.045
2020-02-19	32.8505	32.8915	0.041
2020-02-20	34.3758	34.4123	0.037
2020-02-21	35.1307	35.1633	0.033
2020-02-22	34.7344	34.7628	0.028
2020-02-23	33.8882	33.9124	0.024
2020-02-24	33.6194	33.6388	0.019
2020-02-25	34.3332	34.3477	0.014
2020-02-26	35.7672	35.7779	0.011
2020-02-27	37.2924	37.2987	0.0063
2020-02-28	38.0474	38.0497	0.0023
2020-02-29	37.6453	37.6469	0.0016
2020-03-01	36.7934	36.7942	0.00083
2020-03-02	36.5189	36.5182	0.00066
2020-03-03	37.2270	37.2249	0.0021
2020-03-04	38.6552	38.6527	0.0025
2020-03-05	40.1747	40.1713	0.0035
2020-03-06	40.9239	40.9199	0.0040
2020-03-07	40.5219	40.5171	0.0048
2020-03-08	39.6699	39.6644	0.0055
2020-03-09	39.3954	39.3885	0.0070
2020-03-10	40.1035	40.0951	0.0084
2020-03-11	41.5317	41.5230	0.0088
2020-03-12	43.0513	43.0415	0.0098
2020-03-13	43.8005	43.7902	0.010
2020-03-14	43.3984	43.3873	0.011
2020-03-15	42.5465	42.5347	0.012
2020-03-16	42.2720	42.2587	0.013
2020-03-17	42.9801	42.9653	0.015
2020-03-18	44.4083	44.3932	0.015
2020-03-19	45.9278	45.9117	0.016
2020-03-20	46.6770	46.6604	0.017
2020-03-21	46.2749	46.2576	0.017
2020-03-22	45.4230	45.4049	0.018
2020-03-23	45.1485	45.1289	0.020
2020-03-24	45.8566	45.8355	0.021
2020-03-25	47.2848	47.2633	0.021
2020-03-26	48.8043	48.7819	0.022
2020-03-27	49.5535	49.5305	0.023
2020-03-28	49.1515	49.1277	0.024
2020-03-29	48.2995	48.2750	0.025
2020-03-30	48.0250	47.9990	0.026
2020-03-31	48.7331	48.7056	0.028
2020-04-01	50.1613	50.1334	0.028
2020-04-02	51.6809	51.6520	0.029
2020-04-03	52.4301	52.4006	0.029
2020-04-04	52.0280	51.9973	0.031
2020-04-05	51.1761	51.1442	0.032
2020-04-06	50.9016	50.8677	0.034
2020-04-07	51.6097	51.5739	0.036
2020-04-08	53.0379	53.0013	0.037
2020-04-09	54.5574	54.5193	0.038
2020-04-10	55.3066	55.2675	0.039
2020-04-11	54.9046	54.8642	0.040
2020-04-12	54.0526	54.0111	0.042
2020-04-13	53.7781	53.7346	0.044
2020-04-14	54.4862	54.4408	0.045
2020-04-15	55.9144	55.8682	0.046
2020-04-16	57.4340	57.3862	0.048
2020-04-17	58.1832	58.1344	0.049
2020-04-18	57.7811	57.7311	0.050
2020-04-19	56.9292	56.8779	0.051
2020-04-20	56.6547	56.6015	0.053
2020-04-21	57.3628	57.3076	0.055
2020-04-22	58.7910	58.7350	0.056
2020-04-23	60.3105	60.2531	0.057
2020-04-24	61.0597	61.0012	0.058
2020-04-25	60.6576	60.5979	0.060
2020-04-26	59.8057	59.7448	0.061
2020-04-27	59.5312	59.4683	0.063
2020-04-28	60.2393	60.1745	0.065
2020-04-29	61.6675	61.6019	0.066
2020-04-30	63.1870	63.1199	0.067
2020-05-01	63.9362	63.8681	0.068
2020-05-02	63.5342	63.4648	0.069
2020-05-03	62.6822	62.6116	0.071
2020-05-04	62.4077	62.3352	0.073
2020-05-05	63.1158	63.0413	0.074
2020-05-06	64.5440	64.4687	0.075
2020-05-07	66.0636	65.9867	0.077
2020-05-08	66.8128	66.7349	0.078
2020-05-09	66.3584	66.2942	0.064
2020-05-10	65.4542	65.4036	0.051
2020-05-11	65.1274	65.0897	0.038
2020-05-12	65.7831	65.7584	0.025
2020-05-13	67.1590	67.1484	0.011
2020-05-14	68.6263	68.6290	0.0027
2020-05-15	69.3232	69.3397	0.017
2020-05-16	68.8688	68.8990	0.030
2020-05-17	67.9645	68.0084	0.044
2020-05-18	67.6377	67.6945	0.057
2020-05-19	68.2935	68.3632	0.070
2020-05-20	69.6694	69.7532	0.084
2020-05-21	71.0405	71.1192	0.079
2020-05-22	71.6413	71.7155	0.074
2020-05-23	71.0908	71.1602	0.069
2020-05-24	70.0905	70.1551	0.065
2020-05-25	69.6675	69.7266	0.059
2020-05-26	70.2272	70.2808	0.054
2020-05-27	71.5070	71.5562	0.049
2020-05-28	72.8781	72.9223	0.044
2020-05-29	73.4789	73.5185	0.040
2020-05-30	72.9284	72.9633	0.035
2020-05-31	71.9280	71.9581	0.030
2020-06-01	71.4440	71.4733	0.029
2020-06-02	71.9427	71.9710	0.028
2020-06-03	73.1614	73.1900	0.029
2020-06-04	74.4715	74.4996	0.028
2020-06-05	75.0112	75.0394	0.028
2020-06-06	74.3997	74.4277	0.028
2020-06-07	73.3383	73.3661	0.028
2020-06-08	72.8543	72.8812	0.027
2020-06-09	73.3529	73.3790	0.026
2020-06-10	74.5717	74.5979	0.026
2020-06-11	75.8817	75.9076	0.026
2020-06-12	76.4215	76.4474	0.026
2020-06-13	75.8099	75.8356	0.026
2020-06-14	74.7485	74.7741	0.026
2020-06-15	74.2646	74.2892	0.025
2020-06-16	74.7632	74.7870	0.024
2020-06-17	75.9819	76.0059	0.024
2020-06-18	77.2920	77.3155	0.024
2020-06-19	77.8317	77.8553	0.024
2020-06-20	77.2202	77.2436	0.023
2020-06-21	76.1588	76.1820	0.023
2020-06-22	75.6748	75.6972	0.022
2020-06-23	76.1734	76.1949	0.022
2020-06-24	77.3922	77.4139	0.022
2020-06-25	78.7022	78.7235	0.021
2020-06-26	79.2420	79.2633	0.021
2020-06-27	78.6304	78.6516	0.021
2020-06-28	77.5690	77.5900	0.021
2020-06-29	77.0851	77.1051	0.020
2020-06-30	77.5837	77.6029	0.019
2020-07-01	78.8024	78.8219	0.019
2020-07-02	80.1125	80.1315	0.019
2020-07-03	80.6522	80.6713	0.019
2020-07-04	80.0407	80.0596	0.019
2020-07-05	78.9793	78.9980	0.019
2020-07-06	78.4953	78.5131	0.018
2020-07-07	78.9940	79.0109	0.017
2020-07-08	80.2127	80.2298	0.017
2020-07-09	81.5228	81.5395	0.017
2020-07-10	82.0625	82.0792	0.017
2020-07-11	81.4510	81.4675	0.017
2020-07-12	80.3896	80.4060	0.016
2020-07-13	79.9056	79.9211	0.015
2020-07-14	80.4042	80.4188	0.015
2020-07-15	81.6230	81.6378	0.015
2020-07-16	82.9330	82.9474	0.014
2020-07-17	83.4728	83.4872	0.014
2020-07-18	82.8612	82.8755	0.014
2020-07-19	81.7998	81.8139	0.014
2020-07-20	81.3159	81.3291	0.013
2020-07-21	81.8145	81.8268	0.012
2020-07-22	83.0332	83.0458	0.013
2020-07-23	84.3433	84.3554	0.012
2020-07-24	84.8830	84.8952	0.012
2020-07-25	84.2715	84.2835	0.012
2020-07-26	83.2101	83.2219	0.012
2020-07-27	82.7261	82.7370	0.011
2020-07-28	83.2247	83.2348	0.010
2020-07-29	84.4435	84.4537	0.010
2020-07-30	85.7535	85.7634	0.0098
2020-07-31	86.2933	86.3032	0.0099
2020-08-01	85.6817	85.6914	0.0097
2020-08-02	84.6203	84.6299	0.0095
2020-08-03	84.1364	84.1450	0.0086
2020-08-04	84.6350	84.6428	0.0078
2020-08-05	85.8537	85.8617	0.0080
2020-08-06	87.1638	87.1713	0.0075
2020-08-07	87.7035	87.7111	0.0076
2020-08-08	87.0920	87.0994	0.0074
2020-08-09	86.0306	86.0378	0.0072
2020-08-10	85.5466	85.5530	0.0063
2020-08-11	86.0453	86.0507	0.0055
2020-08-12	87.2640	87.2697	0.0057
2020-08-13	88.5741	88.5793	0.0052
2020-08-14	89.1138	89.1191	0.0053
2020-08-15	88.5023	88.5074	0.0051
2020-08-16	87.4409	87.4458	0.0049
2020-08-17	86.9569	86.9609	0.0040
2020-08-18	87.4555	87.4587	0.0032
2020-08-19	88.6743	88.6776	0.0034
2020-08-20	89.9843	89.9873	0.0030
2020-08-21	90.5240	90.5271	0.0030
2020-08-22	89.9125	89.9153	0.0028
2020-08-23	88.8511	88.8538	0.0027
2020-08-24	88.3672	88.3689	0.0017
2020-08-25	88.8658	88.8667	0.00089
2020-08-26	90.0845	90.0856	0.0011
2020-08-27	91.3946	91.3952	0.00067
2020-08-28	91.9343	91.9350	0.00072
2020-08-29	91.3228	91.3233	0.00053
2020-08-30	90.2614	90.2617	0.00036
2020-08-31	89.7774	89.7769	0.00054
2020-09-01	90.2760	90.2746	0.0014
2020-09-02	91.5790	91.5653	0.014
2020-09-03	92.9733	92.9467	0.027
2020-09-04	93.5973	93.5582	0.039
2020-09-05	93.0700	93.0182	0.052
2020-09-06	92.0929	92.0284	0.064
2020-09-07	91.6931	91.6153	0.078
2020-09-08	92.2760	92.1848	0.091
2020-09-09	93.5790	93.4755	0.10
2020-09-10	94.9733	94.8569	0.12
2020-09-11	95.5972	95.4684	0.13
2020-09-12	95.0700	94.9284	0.14
2020-09-13	94.0928	93.9386	0.15
2020-09-14	93.8242	93.6817	0.14
2020-09-15	94.5383	94.4075	0.13
2020-09-16	95.9724	95.8544	0.12
2020-09-17	97.4979	97.3920	0.11
2020-09-18	98.2530	98.1598	0.093
2020-09-19	97.8569	97.7761	0.081
2020-09-20	97.0109	96.9425	0.068
2020-09-21	96.7424	96.6857	0.057
2020-09-22	97.4564	97.4114	0.045
2020-09-23	98.8906	98.8584	0.032
2020-09-24	100.4160	100.3960	0.020
2020-09-25	101.1712	101.1638	0.0074
2020-09-26	100.8541	100.8578	0.0037
2020-09-27	100.0871	100.1019	0.015
2020-09-28	99.8975	99.9227	0.025
2020-09-29	100.6906	100.7262	0.036
2020-09-30	102.2037	102.2508	0.047
2020-10-01	103.8082	103.8661	0.058
2020-10-02	104.6423	104.7116	0.069
2020-10-03	104.3252	104.4056	0.080
2020-10-04	103.5583	103.6497	0.091
2020-10-05	103.3687	103.4705	0.10
2020-10-06	104.1617	104.2739	0.11
2020-10-07	105.6947	105.7998	0.11
2020-10-08	107.3191	107.4162	0.097
2020-10-09	108.1730	108.2629	0.090
2020-10-10	107.8758	107.9580	0.082
2020-10-11	107.1286	107.2033	0.075
2020-10-12	106.9589	107.0253	0.066
2020-10-13	107.7718	107.8299	0.058
2020-10-14	109.3048	109.3557	0.051
2020-10-15	110.9291	110.9722	0.043
2020-10-16	111.7831	111.8189	0.036
2020-10-17	111.4858	111.5140	0.028
2020-10-18	110.7386	110.7593	0.021
2020-10-19	110.5689	110.5885	0.020
2020-10-20	111.3818	111.4003	0.018
2020-10-21	112.9148	112.9332	0.018
2020-10-22	114.5392	114.5569	0.018
2020-10-23	115.3932	115.4107	0.018
2020-10-24	115.0959	115.1130	0.017
2020-10-25	114.3488	114.3655	0.017
2020-10-26	114.1791	114.1946	0.016
2020-10-27	114.9920	115.0064	0.014
2020-10-28	116.5250	116.5394	0.014
2020-10-29	118.1493	118.1630	0.014
2020-10-30	119.0033	119.0168	0.014
2020-10-31	118.7060	118.7192	0.013
2020-11-01	117.9589	117.9716	0.013
2020-11-02	117.7892	117.8008	0.012
2020-11-03	118.6021	118.6126	0.010
2020-11-04	120.1351	120.1455	0.010
2020-11-05	121.7594	121.7692	0.0098
2020-11-06	122.6134	122.6230	0.0096
2020-11-07	122.3162	122.3253	0.0091
2020-11-08	121.5690	121.5778	0.0087
2020-11-09	121.3993	121.4069	0.0076
2020-11-10	122.2122	122.2187	0.0065
2020-11-11	123.7452	123.7517	0.0065
2020-11-12	125.3695	125.3753	0.0058
2020-11-13	126.2235	126.2291	0.0056
2020-11-14	125.9263	125.9314	0.0052
2020-11-15	125.1791	125.1839	0.0048
2020-11-16	125.0094	125.0131	0.0036
2020-11-17	125.8223	125.8248	0.0025
2020-11-18	127.3553	127.3578	0.0025
2020-11-19	128.9797	128.9815	0.0018
2020-11-20	129.8337	129.8353	0.0016
2020-11-21	129.5364	129.5376	0.0012
2020-11-22	128.7893	128.7901	0.00079
2020-11-23	128.6196	128.6192	0.00036
2020-11-24	129.4325	129.4310	0.0015
2020-11-25	130.9655	130.9640	0.0015
2020-11-26	132.5898	132.5876	0.0022
2020-11-27	133.4438	133.4414	0.0023
2020-11-28	133.1465	133.1437	0.0028
2020-11-29	132.3994	132.3962	0.0032
2020-11-30	132.2297	132.2254	0.0043
2020-12-01	133.0426	133.0371	0.0054
2020-12-02	134.5756	134.5701	0.0055
2020-12-03	136.1999	136.1938	0.0061
2020-12-04	137.0539	137.0476	0.0063
2020-12-05	136.7567	136.7499	0.0068
2020-12-06	136.0095	136.0024	0.0072
2020-12-07	135.8398	135.8315	0.0083
2020-12-08	136.6527	136.6433	0.0094
2020-12-09	138.1857	138.1763	0.0094
2020-12-10	139.8100	139.7999	0.010
2020-12-11	140.6640	140.6537	0.010
2020-12-12	140.3668	140.3560	0.011
2020-12-13	139.6196	139.6085	0.011
2020-12-14	139.4499	139.4377	0.012
2020-12-15	140.2628	140.2494	0.013
2020-12-16	141.7958	141.7824	0.013
2020-12-17	143.4202	143.4061	0.014
2020-12-18	144.2742	144.2599	0.014
2020-12-19	143.9769	143.9622	0.015
2020-12-20	143.2298	143.2147	0.015
2020-12-21	143.0601	143.0438	0.016
2020-12-22	143.8730	143.8556	0.017
2020-12-23	145.4060	145.3886	0.017
2020-12-24	147.0303	147.0122	0.018
2020-12-25	147.8843	147.8660	0.018
2020-12-26	147.5870	147.5683	0.019
2020-12-27	146.8399	146.8208	0.019
2020-12-28	146.6702	146.6500	0.020
2020-12-29	147.4831	147.4617	0.021
2020-12-30	149.0161	148.9947	0.021

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)	-1465.4840	-1466.4526	0.01

Timing

Median of all measured repetitions.

Step	Effect Prophet	Python Prophet	Effect Prophet is
Fit	7.36 ms	30.1 ms	4.1× faster
Simulate uncertainty	13.0 ms	167 ms	Not compared: different work
Fit and find anomalies	25.2 ms	199 ms	7.9× 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": "linear-output-first-v4"
  },
  "fitRequest": "growth-only",
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    "holidaysMode": "additive",
    "changepoints": {
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    ],
    "events": [],
    "regressors": []
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  "pythonOptimizer": {
    "algorithm": "Auto",
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  },
  "uncertainty": {
    "seed": 19,
    "samples": 1000,
    "intervalWidth": 0.99,
    "output": "intervals",
    "algorithm": "scalar-continuous-time",
    "evidence": "docs/validation/uncertainty.md#evidence-classes",
    "samplerMemoryLimitBytes": 67108864
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  "anomalies": {
    "expected": [
      "2020-02-20T00:00:00.000Z",
      "2020-04-30T00:00:00.000Z",
      "2020-08-18T00:00:00.000Z",
      "2020-10-27T00:00:00.000Z"
    ]
  }
}