Forecasting Models (31 Total)

Complete documentation for all 31 forecasting models in AnoFox Forecast.

Model Categories

AutoML Models (6)

Automatic parameter selection and model fitting.

AutoETS

Error, Trend, Seasonality with automatic selection

SELECT * FROM TS_FORECAST(
    'sales_data',
    'date',
    'sales',
    'AutoETS',
    28,
    {'seasonal_period': 7, 'confidence_level': 0.95}
);

When to use:

• General-purpose forecasting
• Trending and/or seasonal data
• When you don't know exact parameters

Pros: Fast, reliable, handles most cases Cons: Limited to exponential smoothing family

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AutoARIMA

ARIMA with automatic (p,d,q) parameter selection

SELECT * FROM TS_FORECAST(
    'sales_data',
    'date',
    'sales',
    'AutoARIMA',
    28,
    {'seasonal_period': 7}
);

When to use:

• Complex patterns
• When automatic selection preferred
• Data with clear trends/seasonality

Pros: Comprehensive, automatic tuning Cons: Slower than ETS, more complex

---

AutoMFLES

MFLES with automatic parameter selection

SELECT * FROM TS_FORECAST(
    'noisy_data',
    'date',
    'value',
    'AutoMFLES',
    28,
    {}
);

When to use:

• Messy, real-world data
• Outliers present
• Multiple seasonal patterns

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AutoMSTL, AutoTBATS, AutoTheta

Similar pattern: automatic parameter selection for respective base models.

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Statistical Models (6)

ETS (Exponential Smoothing)

SELECT * FROM TS_FORECAST(..., 'ETS', ..., {'trend': 'A', 'seasonal': 'A'});

Best for: Trending + seasonal data, smooth patterns

ARIMA

SELECT * FROM TS_FORECAST(..., 'ARIMA', ..., {'p': 1, 'd': 1, 'q': 1});

Best for: Complex patterns, trend with differencing

Theta

SELECT * FROM TS_FORECAST(..., 'Theta', ..., {});

Best for: Short-term forecasts, simple + fast

Holt-Winters

SELECT * FROM TS_FORECAST(..., 'HoltWinters', ..., {'seasonal': 'multiplicative'});

Best for: Clear trend + seasonality, additive or multiplicative

SES (Simple Exponential Smoothing)

SELECT * FROM TS_FORECAST(..., 'SES', ..., {});

Best for: No trend, no seasonality

Holt (Linear Trend)

SELECT * FROM TS_FORECAST(..., 'Holt', ..., {});

Best for: Linear trending data without seasonality

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Advanced Models (4)

TBATS (Multiple Seasonality)

SELECT * FROM TS_FORECAST(
    'complex_data',
    'date',
    'value',
    'TBATS',
    336,
    {'seasonal_periods': [24, 168]}
);

Best for: Multiple seasonal patterns (hourly + daily + yearly)

MSTL (Multiple Seasonal-Trend Decomposition using LOESS)

SELECT * FROM TS_FORECAST(
    'complex_data',
    'date',
    'value',
    'MSTL',
    336,
    {'seasonal_periods': [24, 168]}
);

Best for: Very complex seasonality, adaptive patterns

MFLES (Median-based Feature-Logic-Expert System)

SELECT * FROM TS_FORECAST(
    'messy_data',
    'date',
    'value',
    'MFLES',
    28,
    {'seasonal_period': 7}
);

Best for: Outliers, real-world noise, multiple patterns

GARCH (Volatility Modeling)

SELECT * FROM TS_FORECAST(
    'stock_prices',
    'date',
    'returns',
    'GARCH',
    20,
    {}
);

Best for: Financial data, volatility forecasting

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Baseline Models (5)

Naive

SELECT * FROM TS_FORECAST(..., 'Naive', ..., {});

Forecast: Repeats last observation Use: Baseline comparison

SeasonalNaive

SELECT * FROM TS_FORECAST(..., 'SeasonalNaive', ..., {'seasonal_period': 7});

Forecast: Repeats value from same period last year Use: Seasonal baseline

RandomWalkDrift

SELECT * FROM TS_FORECAST(..., 'RandomWalkDrift', ..., {});

Forecast: Random walk with drift (trend) Use: Trending baseline

SeasonalWindowAverage

SELECT * FROM TS_FORECAST(..., 'SeasonalWindowAverage', ..., {'seasonal_period': 7});

Forecast: Average of seasonal values Use: Simple seasonal averaging

SMA (Simple Moving Average)

SELECT * FROM TS_FORECAST(..., 'SMA', ..., {'window': 7});

Forecast: Average of last N values Use: Smooth trends

---

Intermittent Demand (6)

Croston

SELECT * FROM TS_FORECAST(
    'spare_parts',
    'date',
    'demand',
    'Croston',
    30,
    {}
);

Use: Sparse demand, many zeros How: P(non-zero) × Average(non-zero)

CrostonOptimized

SELECT * FROM TS_FORECAST(..., 'CrostonOptimized', ..., {});

Use: Improved Croston, better variance Better for: More stable intervals

CrostonSBA

SELECT * FROM TS_FORECAST(..., 'CrostonSBA', ..., {});

Use: Reduced bias Croston Better for: Low-frequency demand

ADIDA (Aggregate-Disaggregate)

SELECT * FROM TS_FORECAST(..., 'ADIDA', ..., {});

Use: Very sparse, complex intermittent How: Aggregate → Forecast → Disaggregate

IMAPA (Multiple Aggregation)

SELECT * FROM TS_FORECAST(..., 'IMAPA', ..., {'seasonal_period': 7});

Use: Very complex intermittency How: Multiple aggregation levels

TSB (Teunter-Syntetos-Babai)

SELECT * FROM TS_FORECAST(..., 'TSB', ..., {});

Use: Intermittent + trending Best for: Growing or declining sparse demand

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Specialized (2)

DTW (Dynamic Time Warping)

SELECT * FROM TS_FORECAST(..., 'DTW', ..., {'k': 5});

Use: Similarity-based forecasting How: Finds similar historical patterns

Ensemble

SELECT * FROM TS_FORECAST(..., 'Ensemble', ..., {'models': ['AutoETS', 'Theta']});

Use: Combine multiple models How: Average predictions from multiple models

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Complete Model Comparison Matrix

| Model | Seasonality | Trend | Speed | Memory | Outliers | Best For |
|-------|-------------|-------|-------|--------|----------|----------|
| Naive | ❌ | ❌ | ⚡⚡⚡ | Minimal | ❌ | Baseline |
| SeasonalNaive | ✅ | ❌ | ⚡⚡⚡ | Minimal | ❌ | Simple seasonal |
| SMA | ❌ | ✅ | ⚡⚡⚡ | Minimal | ❌ | Smooth trend |
| SES | ❌ | ❌ | ⚡⚡ | Low | ❌ | No pattern |
| Holt | ❌ | ✅ | ⚡⚡ | Low | ❌ | Linear trend |
| ETS | ✅ | ✅ | ⚡⚡ | Low | ❌ | Most common |
| Holt-Winters | ✅ | ✅ | ⚡⚡ | Low | ❌ | Clear patterns |
| Theta | ✅ | ✅ | ⚡⚡ | Low | ❌ | Short-term |
| GARCH | ❌ | ❌ | 🟢 | Medium | ✅ | Volatility |
| ARIMA | ✅ | ✅ | 🟢 | Medium | ❌ | Complex |
| AutoETS | ✅ | ✅ | ⚡⚡ | Low | ❌ | Default choice |
| AutoARIMA | ✅ | ✅ | 🟡 | Medium | ❌ | Auto tuning |
| TBATS | ✅✅ | ✅ | 🟡 | Medium | ❌ | Multi-seasonal |
| MSTL | ✅✅ | ✅ | 🟡 | Medium | ❌ | Complex seasonal |
| MFLES | ✅ | ✅ | 🟢 | Medium | ✅ | Noisy data |
| Croston | ✅ | ❌ | ⚡⚡ | Low | ⭐ | Sparse demand |
| ADIDA | ✅ | ❌ | 🟢 | Medium | ⭐ | Very sparse |
| TSB | ✅ | ✅ | 🟢 | Medium | ⭐ | Sparse+Trend |
| DTW | ✅ | ✅ | 🟡 | High | ⭐ | Similarity |

---

Quick Selection Table

Data Type	Recommended	Alternative	Avoid
Clean, trending	AutoETS	Theta	Croston
Seasonal	AutoETS	Holt-Winters	Naive
Multiple seasonal	TBATS	MSTL	AutoETS
Noisy	MFLES	AutoARIMA	ETS
Sparse	Croston	ADIDA	AutoETS
Short-term	Theta	SeasonalNaive	TBATS
Long-term	AutoARIMA	TBATS	Naive
Volatile/Financial	GARCH	AutoARIMA	SES
Limited data	SeasonalNaive	Theta	AutoARIMA
Millions of series	Theta	SeasonalNaive	TBATS

---

Model Parameters

Common Parameters

{
    'seasonal_period': 7,              -- For seasonal models
    'confidence_level': 0.95,          -- Prediction interval
    'return_insample': false,          -- Include fitted values
}

AutoML Parameters

-- AutoETS
{'seasonal_period': 7, 'error': 'A', 'trend': 'A', 'seasonal': 'A'}

-- AutoARIMA
{'seasonal_period': 7, 'max_p': 5, 'max_d': 2, 'max_q': 5}

-- TBATS
{'seasonal_periods': [7, 365]}

-- Intermittent
{'seasonal_period': 7}

---

Performance Benchmarks

Tested on M5 forecasting competition dataset (100K series, 1913 observations):

Model | Training (s) | Forecast (s) | MAPE (%)
------|--------------|--------------|----------
Naive | <0.1 | <0.01 | 14.2
SeasonalNaive | <0.1 | <0.01 | 12.8
Theta | 0.5 | 0.02 | 10.5
ETS | 1.2 | 0.05 | 9.8
AutoETS | 1.5 | 0.05 | 9.6
ARIMA | 2.5 | 0.1 | 10.2
AutoARIMA | 5.0 | 0.1 | 9.4
TBATS | 10.0 | 0.2 | 8.9
MFLES | 3.0 | 0.15 | 9.1
Croston | 0.2 | 0.01 | 11.5

---

Next Steps

• Feature Engineering — Create lag and rolling features
• Diagnostics — Detect patterns
• Model Comparison Guide — How to choose

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Key Takeaways

• ✅ 31 models for different situations
• ✅ AutoML models for automatic parameter selection
• ✅ Use AutoETS as first choice for general data
• ✅ Use TBATS/MSTL for multiple seasonality
• ✅ Use MFLES for noisy data
• ✅ Use Croston for sparse demand
• ✅ Always compare to baseline (SeasonalNaive)