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

# Cross-validation with a forecast regressor

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

Two cutoffs and a 7-day horizon, fitting the temperature model again in each fold. Python's cross_validation refits it on standardized values and drifts by about 15% here, so Python is fitted at each cutoff instead.

## Input

[`benchmark/inputs/v4/flat-correlated-regressors.json`](https://github.com/jer-k/effect-prophet/blob/main/benchmark/inputs/v4/flat-correlated-regressors.json): 730 history rows and 180 forecast rows.

## Output

Largest difference: **0.012** (0.094% 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 |
| --- | ---: | ---: | ---: | ---: |
| 2021-12-03 | 45.5639 | 46.0110 | 46.0220 | 0.011 |
| 2021-12-04 | 43.8466 | 44.6465 | 44.6576 | 0.011 |
| 2021-12-05 | 43.2507 | 43.1670 | 43.1783 | 0.011 |
| 2021-12-06 | 43.8873 | 42.6254 | 42.6368 | 0.011 |
| 2021-12-07 | 44.4927 | 43.3799 | 43.3915 | 0.012 |
| 2021-12-08 | 45.2585 | 44.8417 | 44.8539 | 0.012 |
| 2021-12-09 | 46.2383 | 45.8664 | 45.8788 | 0.012 |
| 2021-12-17 | 45.5393 | 45.2172 | 45.2096 | 0.0076 |
| 2021-12-18 | 43.9466 | 43.8397 | 43.8323 | 0.0074 |
| 2021-12-19 | 42.8487 | 42.3669 | 42.3597 | 0.0071 |
| 2021-12-20 | 43.5652 | 41.8428 | 41.8358 | 0.0070 |
| 2021-12-21 | 44.6979 | 42.5891 | 42.5822 | 0.0069 |
| 2021-12-22 | 45.2593 | 44.0291 | 44.0213 | 0.0078 |
| 2021-12-23 | 45.8218 | 45.0435 | 45.0356 | 0.0079 |

## Timing

Median of all measured repetitions.

| Step | Effect Prophet | Python Prophet | Effect Prophet is |
| --- | ---: | ---: | --- |
| Convert input rows | 250 µs | 750 µs | Not compared: different work |
| Plan cross-validation folds | 2.61 ms | 1.01 ms | Not compared: different work |
| Cross-validate | 60.3 ms | 227 ms | Not compared: different work |
| Compute metrics | 98 µs | 5.25 ms | Not compared: different work |
| Score baselines | 7.10 ms | 2.00 ms | Not compared: different work |
| First cross-validation in a new process | 260 ms | 1.64 s | 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.

* **Convert input rows, Plan cross-validation folds, Cross-validate, Compute metrics, Score baselines, First cross-validation in a new process:** 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": "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",
        "predictor": true
      },
      {
        "name": "baseline",
        "priorScale": 10,
        "standardization": "never"
      }
    ]
  },
  "pythonOptimizer": {
    "algorithm": "Auto",
    "maxIterations": 10000,
    "newtonFallback": true,
    "sigFigs": 12
  },
  "plan": {
    "horizonMs": 604800000,
    "cutoffs": [
      "2021-12-02T00:00:00.000Z",
      "2021-12-16T00:00:00.000Z"
    ]
  },
  "metricAggregation": "horizons"
}
```