Intermittent Demand Models

AnoFox provides 6 intermittent demand models: 3 Croston variants (Classic, Optimized, SBA with bias correction), ADIDA for very sparse demand, IMAPA for complex multi-temporal intermittency, and TSB for trending sparse patterns. These models are designed for data with high zero percentages -- spare parts inventory, low-volume SKUs, and irregular service demand -- where standard ETS or ARIMA models produce unreliable forecasts. CrostonSBA is the recommended default for most intermittent demand scenarios due to its bias correction.

Intermittent demand refers to demand patterns characterized by frequent zero-demand periods interspersed with irregular, often variable-sized orders. These specialized models handle sparse, lumpy demand patterns that standard forecasting methods like ETS or ARIMA struggle with.

Model	Description
CrostonClassic	Classic Croston method for sparse demand
CrostonOptimized	Croston with optimized smoothing parameters
CrostonSBA	Syntetos-Boylan Approximation (bias-corrected)
ADIDA	Aggregate-Disaggregate Intermittent Demand
IMAPA	Intermittent Multiple Aggregation Prediction
TSB	Teunter-Syntetos-Babai (trending intermittent)

Showing 6 of 6

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CrostonClassic

The Croston method is a forecasting approach designed for intermittent demand that decomposes the problem into two components: the size of non-zero demands and the interval between consecutive non-zero demands. Each component is forecast separately using exponential smoothing, and the final demand rate is their ratio. This classic variant separately forecasts demand size and inter-arrival times.

Example

SELECT * FROM ts_forecast_by(
    'spare_parts', NULL, date, demand,
    'CrostonClassic', 30, '1d',
    MAP{}
);

Best for: Sparse demand, many zeros, spare parts inventory.

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CrostonOptimized

Croston method with optimized smoothing parameters.

Example

SELECT * FROM ts_forecast_by(
    'spare_parts', NULL, date, demand,
    'CrostonOptimized', 30, '1d',
    MAP{}
);

Best for: Better variance estimation than classic Croston.

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CrostonSBA

Syntetos-Boylan Approximation (SBA) - a bias-corrected variant of Croston's method.

Example

SELECT * FROM ts_forecast_by(
    'low_frequency', NULL, date, demand,
    'CrostonSBA', 30, '1d',
    MAP{}
);

Best for: Reduced bias, low-frequency demand.

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ADIDA

Aggregate-Disaggregate Intermittent Demand Approach.

Example

SELECT * FROM ts_forecast_by(
    'very_sparse', NULL, date, demand,
    'ADIDA', 30, '1d',
    MAP{}
);

Best for: Very sparse demand, complex intermittent patterns.

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IMAPA

Intermittent Multiple Aggregation Prediction Algorithm.

Example

SELECT * FROM ts_forecast_by(
    'complex_intermittent', NULL, date, demand,
    'IMAPA', 30, '1d',
    MAP{}
);

Best for: Very complex intermittency, multiple temporal patterns.

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TSB

Teunter-Syntetos-Babai (TSB) method - handles trending intermittent demand.

Example

SELECT * FROM ts_forecast_by(
    'trending_sparse', NULL, date, demand,
    'TSB', 30, '1d',
    MAP{}
);

Best for: Intermittent + trending, growing/declining sparse demand.

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Comparison

Model	Trend Support	Bias Correction	Complexity
CrostonClassic	No	No	Simple
CrostonOptimized	No	No	Simple
CrostonSBA	No	Yes	Simple
ADIDA	No	Moderate	Medium
IMAPA	No	Yes	Complex
TSB	Yes	Yes	Medium

Demand Classification

Before choosing a model, classify your demand pattern:

Pattern	Zero %	Variation	Recommended
Smooth	Low	Low	AutoETS
Erratic	Low	High	MFLES
Intermittent	High	Low	CrostonSBA
Lumpy	High	High	TSB or ADIDA

When to Use Intermittent Models

Scenario	Recommended Model
Spare parts inventory	CrostonClassic
Low-frequency demand	CrostonSBA
Very sparse (>80% zeros)	ADIDA
Complex intermittency	IMAPA
Growing/declining sparse	TSB
Quick baseline	CrostonClassic

The demand classification approach is critical for intermittent series: use the zero percentage as a primary selector. Below 30% zeros, standard models like AutoETS or MFLES perform well. Between 30-70% zeros, CrostonClassic or CrostonSBA are appropriate. Above 70% zeros, ADIDA or IMAPA handle the extreme sparsity. TSB is the only intermittent model that handles trending demand, making it essential for products with growing or declining order patterns.

Example: Spare Parts Forecasting

-- Classify demand first
WITH classified AS (
    SELECT
        sku_id,
        COUNT(*) as n_obs,
        SUM(CASE WHEN demand = 0 THEN 1 ELSE 0 END)::DOUBLE / COUNT(*) as zero_pct
    FROM spare_parts_demand
    GROUP BY sku_id
)
-- Use appropriate model based on zero percentage
SELECT
    sku_id,
    CASE
        WHEN zero_pct > 0.7 THEN 'CrostonSBA'
        WHEN zero_pct > 0.3 THEN 'CrostonClassic'
        ELSE 'AutoETS'
    END as recommended_model
FROM classified;

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Frequently Asked Questions

How do I know if my demand is "intermittent" enough for these models?

If more than 30% of your observations are zero, consider intermittent demand models. Classify your demand using the ADI (Average Demand Interval) and CV (Coefficient of Variation) metrics. High ADI with low CV indicates intermittent demand (use CrostonSBA). High ADI with high CV indicates lumpy demand (use TSB or ADIDA). The Demand Classification table above provides thresholds.

Why does Croston tend to overestimate demand?

Classic Croston has a known positive bias because it estimates demand size and interval independently, then divides them. The ratio of two separately smoothed estimates introduces systematic upward bias. CrostonSBA (Syntetos-Boylan Approximation) applies a correction factor to remove this bias, making it the preferred default for most intermittent demand scenarios.

Can I use these models with grouped data (e.g., per SKU)?

Yes. All intermittent models work with ts_forecast_by which supports the group_col parameter. Pass your SKU or product column as the group column and the function fits a separate model for each group automatically. Use NULL for the group column if you have a single series.

When should I use TSB instead of Croston variants?

Use TSB (Teunter-Syntetos-Babai) when your intermittent demand has a trend -- either growing or declining over time. Croston and its variants assume a stationary demand rate, so they cannot capture systematic changes. TSB explicitly models the demand probability as time-varying, making it the only intermittent model in this set that handles trending sparse demand.