anofox-forecast 0.15.9

Time series forecasting library
Documentation 
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# Full Validation: anofox-forecast (Rust) vs statsforecast (Python)

Comprehensive comparison of forecast accuracy and speed across all major model families.

## Test Setup

- **Rust**: anofox-forecast v0.5.5, release build, single-threaded (no `parallel` feature)
- **Python**: statsforecast (Nixtla), latest version
- **Data**: 5 deterministic synthetic series (flat, trend, seasonal p=12, seasonal p=7, intermittent)
- **Horizon**: 12 steps ahead
- **Metric**: MAD (Mean Absolute Difference between Rust and Python forecasts)

## Accuracy Results

### Flat Series (n=100, no trend, no seasonality)

| Model | MAD | Match | Notes |
|---|---|---|---|
| Naive | 0.0000 | EXACT | |
| RandomWalkWithDrift | 0.0000 | EXACT | |
| SES (α=0.3) | 0.0000 | EXACT | |
| Holt | 0.8393 | CLOSE | Different local optima |
| Theta | 0.0000 | EXACT | |
| OptimizedTheta | 0.0393 | CLOSE | |
| AutoETS | 0.0590 | CLOSE | |
| AutoARIMA | 0.1355 | CLOSE | Different order selected |

### Trend Series (n=100, slope=0.5)

| Model | MAD | Match | Notes |
|---|---|---|---|
| Naive | 0.0000 | EXACT | |
| RandomWalkWithDrift | 0.0000 | EXACT | |
| SES (α=0.3) | 0.0000 | EXACT | |
| Holt | 0.8378 | CLOSE | Different local optima |
| Theta | 1.7236 | OK | Different θ optimization |
| OptimizedTheta | 0.5830 | CLOSE | |
| AutoETS | 0.0010 | EXACT | |
| AutoARIMA | 0.4495 | CLOSE | |

### Seasonal Series (n=120, period=12)

| Model | MAD | Match | Notes |
|---|---|---|---|
| Naive | 0.0000 | EXACT | |
| SeasonalNaive | 0.0000 | EXACT | |
| SES (α=0.3) | 0.0000 | EXACT | |
| Holt | 8.5088 | DIFF | Non-seasonal model on seasonal data |
| Theta | 0.8201 | CLOSE | |
| OptimizedTheta | 0.2481 | CLOSE | |
| AutoETS | 0.1200 | CLOSE | |
| AutoARIMA | 0.4643 | CLOSE | |
| MFLES | 1.0955 | OK | Different boosting convergence |

### Seasonal Series (n=140, period=7)

| Model | MAD | Match | Notes |
|---|---|---|---|
| Naive | 0.0000 | EXACT | |
| SeasonalNaive | 0.0000 | EXACT | |
| SES (α=0.3) | 0.0000 | EXACT | |
| Holt | 4.7465 | OK | Non-seasonal model on seasonal data |
| Theta | 0.3053 | CLOSE | |
| OptimizedTheta | 0.1433 | CLOSE | |
| AutoETS | 0.0465 | CLOSE | |
| AutoARIMA | 0.4781 | CLOSE | |
| MFLES | 1.1325 | OK | Different boosting convergence |

### Intermittent Series (n=60)

| Model | MAD | Match | Notes |
|---|---|---|---|
| CrostonSBA | 0.0805 | CLOSE | |

## Accuracy Summary

| Category | Count | Percentage |
|---|---|---|
| **EXACT** (MAD < 0.01) | 14 | 40% |
| **CLOSE** (MAD < 1.0) | 16 | 46% |
| **OK** (MAD < 5.0) | 4 | 11% |
| **DIFF** (MAD ≥ 5.0) | 1 | 3% |
| **Total** | **35** | |
| **Within MAD < 1.0** | **30/35** | **86%** |
| **Within MAD < 5.0** | **34/35** | **97%** |

The single DIFF case (Holt on seasonal data) is expected — Holt is a non-seasonal model applied to seasonal data, so different optimizers find different local minima.

## Speed Comparison

| Model | Python (ms) | Rust (ms) | Speedup |
|---|---|---|---|
| Naive n=200 | 0.019 | 0.005 | **3.8x** |
| SES n=200 | 0.005 | 0.002 | **2.5x** |
| Holt n=200 | 4.761 | 0.078 | **61x** |
| Theta n=200 | 1.191 | 0.002 | **596x** |
| OptimizedTheta n=200 | 7.636 | 0.272 | **28x** |
| AutoETS n=120 p=12 | 69.150 | 50.921 | **1.4x** |
| AutoARIMA n=200 | 173.390 | 1.860 | **93x** |
| AutoARIMA n=120 p=12 | 564.763 | 28.475 | **20x** |
| CrostonSBA n=60 | 0.045 | 0.014 | **3.2x** |
| MFLES n=120 p=12 | 1.413 | 0.104 | **14x** |

**Geometric mean speedup: ~15x across all models.**

Individual model highlights:
- **Theta**: 596x faster (Python uses optimization, Rust uses closed-form)
- **AutoARIMA nonseasonal**: 93x faster
- **Holt**: 61x faster
- **AutoARIMA seasonal**: 20x faster
- **AutoETS seasonal**: 1.4x faster (both spend time on NM optimization)

## Conclusion

anofox-forecast produces **virtually identical forecasts** to Python statsforecast:
- 86% of models match within MAD < 1.0
- 97% of models match within MAD < 5.0
- The single outlier is Holt on seasonal data (expected different local optima)

Speed: **3-596x faster** depending on model, with geometric mean ~15x. The largest gains are in models with closed-form solutions or efficient optimization (Theta, ARIMA). The smallest gains are in AutoETS where both implementations are dominated by NM optimization.