---
url: >-
  https://jer-k.github.io/effect-prophet/benchmarks/linear/linear-regressor-model.md
---

# A regressor forecast by its own model

  [← All linear growth benchmarks](/benchmarks/linear)

The same four regressors on Prophet's defaults, with the smooth cyclical one forecast by its own default model, as with regressor_predictor=True.

## Input

[`benchmark/inputs/v1/map-regressors-medium.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v1/map-regressors-medium.json): 256 history rows and 64 forecast rows.

## Output

Largest difference: **0.0039** (0.0040% of the input's range).

Every forecast row from both libraries.

| Date | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: |
| 2020-09-13 | 107.1941 | 107.1951 | 0.00099 |
| 2020-09-14 | 107.6427 | 107.6439 | 0.0012 |
| 2020-09-15 | 108.0898 | 108.0913 | 0.0014 |
| 2020-09-16 | 108.5369 | 108.5386 | 0.0017 |
| 2020-09-17 | 107.9404 | 107.9420 | 0.0016 |
| 2020-09-18 | 110.1882 | 110.1900 | 0.0018 |
| 2020-09-19 | 110.6368 | 110.6388 | 0.0020 |
| 2020-09-20 | 111.0853 | 111.0875 | 0.0022 |
| 2020-09-21 | 110.0970 | 110.0991 | 0.0021 |
| 2020-09-22 | 110.5526 | 110.5549 | 0.0023 |
| 2020-09-23 | 111.0126 | 111.0151 | 0.0025 |
| 2020-09-24 | 111.4768 | 111.4796 | 0.0028 |
| 2020-09-25 | 112.3056 | 112.3082 | 0.0026 |
| 2020-09-26 | 112.7799 | 112.7827 | 0.0028 |
| 2020-09-27 | 115.0587 | 115.0616 | 0.0029 |
| 2020-09-28 | 115.5445 | 115.5476 | 0.0031 |
| 2020-09-29 | 116.3966 | 116.3995 | 0.0029 |
| 2020-09-30 | 113.6928 | 113.6960 | 0.0032 |
| 2020-10-01 | 114.1996 | 114.2030 | 0.0034 |
| 2020-10-02 | 114.7136 | 114.7171 | 0.0035 |
| 2020-10-03 | 115.5947 | 115.5980 | 0.0033 |
| 2020-10-04 | 116.1216 | 116.1250 | 0.0034 |
| 2020-10-05 | 116.6573 | 116.6608 | 0.0035 |
| 2020-10-06 | 119.0008 | 119.0044 | 0.0036 |
| 2020-10-07 | 119.9115 | 119.9148 | 0.0034 |
| 2020-10-08 | 120.4694 | 120.4728 | 0.0035 |
| 2020-10-09 | 119.2335 | 119.2371 | 0.0036 |
| 2020-10-10 | 119.8046 | 119.8083 | 0.0037 |
| 2020-10-11 | 120.7398 | 120.7432 | 0.0034 |
| 2020-10-12 | 121.3223 | 121.3258 | 0.0035 |
| 2020-10-13 | 120.5070 | 120.5106 | 0.0036 |
| 2020-10-14 | 121.1003 | 121.1040 | 0.0037 |
| 2020-10-15 | 123.8581 | 123.8614 | 0.0033 |
| 2020-10-16 | 124.4592 | 124.4627 | 0.0034 |
| 2020-10-17 | 125.0634 | 125.0669 | 0.0035 |
| 2020-10-18 | 123.8677 | 123.8713 | 0.0035 |
| 2020-10-19 | 124.8355 | 124.8387 | 0.0032 |
| 2020-10-20 | 125.4447 | 125.4479 | 0.0033 |
| 2020-10-21 | 126.0550 | 126.0583 | 0.0033 |
| 2020-10-22 | 126.6651 | 126.6685 | 0.0034 |
| 2020-10-23 | 127.6341 | 127.6371 | 0.0030 |
| 2020-10-24 | 130.0422 | 130.0453 | 0.0031 |
| 2020-10-25 | 130.6458 | 130.6489 | 0.0031 |
| 2020-10-26 | 129.8449 | 129.8481 | 0.0032 |
| 2020-10-27 | 129.0029 | 129.0058 | 0.0029 |
| 2020-10-28 | 129.5983 | 129.6013 | 0.0030 |
| 2020-10-29 | 130.1891 | 130.1921 | 0.0031 |
| 2020-10-30 | 130.7747 | 130.7779 | 0.0032 |
| 2020-10-31 | 131.7146 | 131.7174 | 0.0029 |
| 2020-11-01 | 132.2868 | 132.2897 | 0.0029 |
| 2020-11-02 | 134.6545 | 134.6575 | 0.0030 |
| 2020-11-03 | 135.2151 | 135.2182 | 0.0031 |
| 2020-11-04 | 136.1292 | 136.1321 | 0.0028 |
| 2020-11-05 | 134.8758 | 134.8788 | 0.0030 |
| 2020-11-06 | 135.4156 | 135.4187 | 0.0031 |
| 2020-11-07 | 135.9478 | 135.9511 | 0.0033 |
| 2020-11-08 | 135.4275 | 135.4306 | 0.0031 |
| 2020-11-09 | 135.9445 | 135.9477 | 0.0032 |
| 2020-11-10 | 136.4541 | 136.4575 | 0.0034 |
| 2020-11-11 | 138.7578 | 138.7613 | 0.0035 |
| 2020-11-12 | 139.6137 | 139.6171 | 0.0033 |
| 2020-11-13 | 140.1032 | 140.1067 | 0.0035 |
| 2020-11-14 | 138.7857 | 138.7894 | 0.0037 |
| 2020-11-15 | 139.2608 | 139.2648 | 0.0039 |

## 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) | -1758.3378 | -1758.3912 | 0.01 |
| Stationarity residual (lower is closer to the best fit) | 16848.4352 | 11056.4239 | 0.01 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Convert input rows | 104 µs | 684 µs | 6.6× faster |
| Fit | 29.8 ms | 101 ms | 3.4× faster |
| Predict | 659 µs | 16.8 ms | 25× faster |
| Fit and predict | 28.6 ms | 119 ms | 4.2× faster |
| Convert, fit and predict | 28.0 ms | 119 ms | 4.2× faster |
| First forecast in a new process | 212 ms | 1.62 s | 7.6× faster |

## Settings

The case declaration both libraries ran.

```json
{
  "kind": "map",
  "comparison": {
    "kind": "equivalent-objective",
    "evidenceId": "linear-output-first-v4"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "auto",
      "count": 25,
      "range": 0.8
    },
    "changepointPriorScale": 0.05,
    "seasonalities": [],
    "events": [],
    "regressors": [
      {
        "name": "binary-auto",
        "priorScale": 10,
        "standardization": "auto"
      },
      {
        "name": "numeric-auto",
        "priorScale": 10,
        "standardization": "auto",
        "predictor": true
      },
      {
        "name": "numeric-always",
        "priorScale": 7,
        "standardization": "always"
      },
      {
        "name": "numeric-never",
        "priorScale": 5,
        "standardization": "never"
      }
    ]
  },
  "effectOptimizer": {
    "algorithm": "auto",
    "maxIterations": 10000,
    "fallback": "newton",
    "lbfgs": {
      "historySize": 5,
      "initAlpha": 0.001,
      "tolObj": 1e-12,
      "tolRelObj": 10000,
      "tolGrad": 1e-8,
      "tolRelGrad": 10000000,
      "tolParam": 1e-8
    }
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  }
}
```