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

# Cross-validation with ranges

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

The same folds with 64 simulated futures per fold for interval coverage.

## Input

[`benchmark/inputs/v1/linear-offset-scaling.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v1/linear-offset-scaling.json): 96 history rows and 24 forecast rows.

## Output

Largest difference: **2.9e-11** (< 0.0001% of the input's range).

Each row is one forecast made during cross-validation, next to the value that actually happened.

| Date | Actual | Effect Prophet | Python Prophet | Difference |
| --- | ---: | ---: | ---: | ---: |
| 2020-03-11 | 107.2568 | 107.1688 | 107.1688 | 2.9e-11 |
| 2020-03-12 | 107.4776 | 107.4962 | 107.4962 | 2.9e-11 |
| 2020-03-13 | 107.6213 | 107.7018 | 107.7018 | 2.8e-11 |
| 2020-03-14 | 107.7396 | 107.6554 | 107.6554 | 2.8e-11 |
| 2020-03-15 | 107.6534 | 107.5295 | 107.5295 | 2.7e-11 |
| 2020-03-16 | 107.5228 | 107.5532 | 107.5532 | 2.8e-11 |
| 2020-03-17 | 107.7277 | 107.7317 | 107.7317 | 2.8e-11 |
| 2020-03-18 | 108.1448 | 108.0262 | 108.0262 | 1.8e-11 |
| 2020-03-19 | 108.3767 | 108.3442 | 108.3442 | 1.8e-11 |
| 2020-03-20 | 108.4456 | 108.5444 | 108.5444 | 1.8e-11 |
| 2020-03-21 | 108.5155 | 108.5134 | 108.5134 | 1.7e-11 |
| 2020-03-22 | 108.4600 | 108.3912 | 108.3912 | 1.7e-11 |
| 2020-03-23 | 108.3204 | 108.4014 | 108.4014 | 1.8e-11 |
| 2020-03-24 | 108.4700 | 108.5823 | 108.5823 | 1.8e-11 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Cross-validate with ranges | 10.5 ms | 78.2 ms | Not compared: different work |

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.

* **Cross-validate with ranges:** Python Prophet's cross-validation returns different outputs, and baselines, search and holdout reports have no Python API, so the benchmark times equivalent application code. The two libraries also compute ranges and some metrics differently.

## Settings

The case declaration both libraries ran.

```json
{
  "kind": "evaluation",
  "comparison": {
    "kind": "different-public-work",
    "evidenceId": "rolling-origin-evaluation-v1"
  },
  "configuration": {
    "growth": "linear",
    "scaling": "absmax",
    "seasonalityMode": "additive",
    "holidaysMode": "additive",
    "changepoints": {
      "mode": "explicit",
      "timestamps": [
        "2020-02-10T00:00:00.000Z"
      ]
    },
    "changepointPriorScale": 0.2,
    "seasonalities": [
      {
        "name": "weekly-custom",
        "periodDays": 7,
        "fourierOrder": 2,
        "priorScale": 10
      }
    ],
    "events": [],
    "regressors": []
  },
  "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
  },
  "plan": {
    "horizonMs": 604800000,
    "cutoffs": [
      "2020-03-10T00:00:00.000Z",
      "2020-03-17T00:00:00.000Z"
    ]
  },
  "metricAggregation": "overall",
  "interval": {
    "seed": 19,
    "samples": 64,
    "intervalWidth": 0.8
  }
}
```