Croston's Method: Forecasting Intermittent Demand

The Croston Method is one way to forecast intermittent demand, where many periods have no demand at all. It may help with spare parts planning and stock decisions, but results depend on the item and the data, so test it against your current method before you change stock plans.

Introduction: The Intermittent Demand Challenge

Most businesses face a forecasting paradox with certain inventory items. Spare parts sit unused for months, then suddenly become critical when equipment fails. Specialized products generate zero sales for weeks, followed by occasional bulk orders. Replacement components gather dust until the precise moment a customer needs them urgently.

To see where your own measure is heading, with a likely range, try the free forecasting tool.

Common forecasting methods can struggle with intermittent demand patterns. Moving averages swing between zero and inflated values, and exponential smoothing on a series full of zeros can give unstable forecasts. Organizations may then hold extra safety stock to buffer against uncertainty, tying up working capital while still seeing stockouts when demand arrives.

The Croston Method was designed for intermittent demand. It separates the question into two components: when will demand occur, and how much will be demanded when it does? Whether that helps for a given item depends on the data, which is why the worked example below compares it against a simple baseline.

Better forecasts for intermittent items can lower spare parts carrying costs, reduce obsolescence write-offs, and improve service levels; how much depends on your items and on how poorly they were forecast before, so measure it against your current method.

What is the Croston Method?

The Croston Method does not try to predict the sporadic demand pattern directly. It splits the problem into two components, each smoothed with exponential smoothing:

The Mathematical Foundation

Understanding Croston's mathematical approach clarifies why it succeeds where traditional methods fail:

When demand occurs at time t (demand > 0):

1. Update demand size estimate:
   Z(t) = α × Demand(t) + (1 - α) × Z(t-1)

2. Update interval estimate:
   P(t) = α × (t - t_last) + (1 - α) × P(t-1)
   where t_last = time of previous non-zero demand

3. Calculate forecast:
   Forecast(t) = Z(t) / P(t)

When demand is zero at time t:
   - No updates to Z or P
   - Forecast remains: Forecast(t) = Forecast(t-1)

Where:
- α = smoothing parameter (you choose it; the example below uses 0.20)
- Z(t) = smoothed demand size at time t
- P(t) = smoothed demand interval at time t
- Demand(t) = observed demand at time t

Why Croston Works for Intermittent Demand

Croston's approach treats intermittent demand as a compound problem:

• Eliminates zero-period distortion: By updating estimates only when demand occurs, Croston avoids letting the zeros pull the estimates down the way they do in ordinary smoothing
• Captures frequency changes: Separately tracking intervals enables detection of changing demand patterns (items becoming more or less frequently demanded)
• Stabilizes volatile forecasts: Smoothing each component independently may give more stable predictions than smoothing the erratic combined series
• Provides interpretable components: Decision-makers can read and check the two components separately

Worked Example (Simulated): Croston vs a Simple Mean Forecast

Question: On a made-up intermittent demand series, how did Croston compare with a simple mean forecast on a holdout period?

Inputs: Simulated data, seed 2026. The script makes 48 periods of demand, where each period has a built-in probability of 0.30 of demand, and a demand size is a Poisson draw with mean 4, plus 1. The first 36 periods are the fit set and the last 12 are the test set.

Method: Croston smooths demand size over the nonzero periods and smooths the gap between them (alpha 0.20), then divides the smoothed size by the smoothed gap. The baseline is the mean demand per period in the fit set. Both forecasts are fixed values compared with the test data using mean absolute error (MAE), the average size of the forecast errors.

import numpy as np

seed = 2026
rng = np.random.default_rng(seed)
periods = 48
occurs = rng.random(periods) < 0.30
demand = np.where(occurs, rng.poisson(4, periods) + 1, 0)
train, test = demand[:36], demand[36:]
alpha = 0.20

# Croston: smooth the nonzero sizes and the gaps between nonzero demands
events = np.flatnonzero(train)
size = float(train[events[0]])
gap = float(events[0] + 1)
last = int(events[0])
for i in events[1:]:
    size = alpha * train[i] + (1 - alpha) * size
    gap = alpha * (i - last) + (1 - alpha) * gap
    last = int(i)
croston = size / gap
mean_fc = float(train.mean())  # baseline: mean demand per period

mae_c = float(np.mean(np.abs(test - croston)))
mae_m = float(np.mean(np.abs(test - mean_fc)))

print(f"Simulated data, seed {seed}")
print(f"Training periods: {len(train)}; holdout periods: {len(test)}")
print("Training demand:", ", ".join(map(str, train[:18])))
print("               ", ", ".join(map(str, train[18:])))
print("Holdout demand:", ", ".join(map(str, test)))
print(f"Croston forecast per holdout period: {croston:.3f}")
print(f"Training-mean forecast per holdout period: {mean_fc:.3f}")
print(f"Croston holdout MAE: {mae_c:.3f}")
print(f"Training-mean holdout MAE: {mae_m:.3f}")

Printed output:

Simulated data, seed 2026
Training periods: 36; holdout periods: 12
Training demand: 7, 0, 0, 0, 0, 0, 0, 1, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0
                4, 3, 0, 0, 0, 3, 0, 0, 8, 0, 0, 5, 7, 0, 0, 0, 0, 0
Holdout demand: 0, 0, 0, 0, 0, 0, 5, 0, 3, 0, 0, 11
Croston forecast per holdout period: 2.112
Training-mean forecast per holdout period: 1.306
Croston holdout MAE: 2.639
Training-mean holdout MAE: 2.236

Result: Croston forecast 2.112 units per period, with a test MAE of 2.639. The mean-demand forecast was 1.306 units per period, with a test MAE of 2.236. In this run the simple mean had the lower MAE.

Limit: On one made-up series of 12 test periods this says nothing about which method is better in general. It shows how the numbers are read, not how any real item behaves.

When the Croston Method May Help

Intermittent demand shows up in several business settings. In each one, test Croston against your current forecast method on held-out data before relying on it.

Spare Parts and Service Operations

Croston may help service teams plan spare parts. Measure any change in cost and stock against the current forecast method:

• Capital efficiency: Better forecasts may allow less spare parts inventory at the same availability
• Availability: Parts availability may improve, which you can track as a service measure
• Obsolescence: More accurate forecasting may reduce write-offs from obsolete inventory
• Warranty parts: Manufacturers may use forecasts to size warranty parts allocation

Specialized B2B Distribution

Distributors serving niche markets with intermittent demand patterns may use Croston to plan stock:

• Stocking specialized items: Forecasts may help decide which specialized items are worth stocking
• Availability: Consistent availability of hard-to-forecast items may matter to customers
• Working capital: Compare total inventory carried before and after a change

Medical and Healthcare Supply Chains

Healthcare organizations managing medical supplies, pharmaceuticals, and specialized equipment can face intermittent demand:

Aerospace and Defense

Organizations managing complex equipment with long lifecycles and critical spare parts may use Croston as one input to planning:

• Readiness: Balance operational readiness against excess inventory costs
• Lifecycle cost: Support costs across long equipment lifecycles can be planned from the forecasts
• Contract estimates: Lifecycle support cost estimates may use the forecasts
• Obsolescence management: Balance last-time-buy decisions with actual intermittent demand forecasts

E-Commerce and Retail Long Tail

Online retailers stocking extensive catalogs with many slow-moving SKUs may use Croston to manage long-tail inventory:

• Assortment breadth: Forecasts may help decide how broad a selection is worth stocking
• Marketplace availability: On marketplace platforms, availability of long-tail items may affect seller ratings
• Drop-ship optimization: Better forecasts inform which intermittent items to stock versus drop-ship
• Customer experience: Track "out of stock" experiences on specialized items

Data Requirements for Effective Implementation

Croston Method results depend on the data behind them. The method needs enough history to see several demand events.

Minimum Historical Data

The method needs enough history to estimate both demand size and interval, which means several nonzero demand events. How much history is enough depends on the item, so check each item's forecast on its own past data.

Data Quality Considerations

Beyond quantity, several data quality factors can affect Croston Method results:

1. True Zero Demand vs. Stockouts

Critical distinction: Croston assumes zero-demand periods represent true absence of demand, not stockout-induced censoring. Contamination of zero periods with stockouts can bias forecasts downward:

2. Demand Aggregation Level

The time period granularity changes the intermittency pattern and may change how well Croston works:

• Too granular (daily for slow items): Creates artificial intermittency; many true zeros obscure patterns
• Too aggregated (monthly for moderate items): Smooths out intermittency; traditional methods may suffice
• Choosing a level: Compare forecast error at more than one aggregation level on held-out data

3. Demand Pattern Stability

Croston assumes underlying demand characteristics remain relatively stable. Several business changes can break this assumption:

• Product lifecycle transitions (introduction, maturity, phase-out)
• Installed base changes for spare parts (equipment population growing or declining)
• Competitive dynamics shifts affecting market share
• Supply chain changes affecting customer ordering patterns

When structural changes occur, restart Croston parameter estimation from the post-change period rather than including pre-change data that represents a different demand regime.

4. Promotional and Calendar Effects

The basic Croston Method does not explicitly account for promotional impacts or calendar effects. For intermittent items influenced by these factors:

• Consider excluding promotional periods and forecasting base demand separately
• Adjust forecasts for known future promotional events
• For calendar-sensitive intermittent items (holiday-related), use Croston within seasonal segments

Setting Up the Analysis: Practical Implementation Steps

Implementing the Croston Method involves data preparation, parameter selection, execution, and validation. The steps below walk through each phase.

Step 1: Identify Candidate Items

Not every inventory item needs Croston forecasting. Begin by identifying items with intermittent demand:

For each SKU in inventory:

1. Calculate intermittency metrics:
   ADI = Total periods / Number of non-zero demand periods
   CV² = (Standard deviation / Mean)² of the non-zero demand sizes

2. Classify item:
   Items with long gaps between orders are intermittent.
   If order sizes also vary a lot, demand is lumpy.
   Compare methods on each item's own history.
3. Prioritize by business impact:
   - Calculate inventory investment for Croston-suitable items
   - Identify high-value intermittent items (ABC analysis)
   - Consider stockout cost/criticality
   - Focus initial implementation on high-impact segments

Step 2: Prepare Historical Data

Systematic data preparation establishes the foundation for accurate forecasting:

1. Extract demand history: Collect time-series demand data for identified items, ensuring sufficient history as outlined in data requirements
2. Clean and validate: Identify and handle data quality issues (missing periods, stockouts coded as zeros, obvious errors)
3. Establish baseline period: Define the historical window for initial parameter estimation (long enough to include several demand events)
4. Document assumptions: Record data preparation decisions, adjustments, and quality issues for future reference

Step 3: Select Smoothing Parameters

The smoothing parameter (alpha) controls how quickly the forecast responds to new information. The value you choose affects forecast accuracy:

Parameter Selection Approaches

• Empirical approach: Test multiple alpha values (0.05, 0.10, 0.15, 0.20, 0.30) and select based on historical forecast accuracy metrics
• Optimization approach: Use automated optimization to minimize forecast error across historical data
• Starting values: Small values such as 0.10 to 0.20 are a common place to begin; the right value depends on the data
• Differential smoothing: Advanced implementation may use different alphas for size versus interval components

Step 4: Initialize Croston Parameters

Croston requires initial estimates for demand size and interval before beginning iterative updates:

Initialization approach (using first N periods for initialization):

Method 1: Simple Averages
- Z(0) = Mean of non-zero demands in initialization period
- P(0) = Mean interval between non-zero demands in initialization period

Method 2: Weighted Recent
- Z(0) = Weighted average favoring recent non-zero demands
- P(0) = Weighted average favoring recent intervals

Method 3: First Occurrence
- Z(0) = First observed non-zero demand
- P(0) = Interval to first demand occurrence

Suggestion: Method 1 (simple averages) is a reasonable default unless
you have reason to believe recent patterns differ from historical ones.

Step 5: Execute Croston Forecasting

An analytics platform can run Croston from a conversational request. The output below is an illustration with made-up numbers, not a result from real data:

User: "Apply Croston Method to forecast demand for our spare parts SKUs. We have 36 months of weekly demand data. Focus on items with intermittent demand patterns and optimize for inventory planning."

Claude: "I'll analyze your spare parts demand using the Croston Method to generate forecasts for intermittent demand items."

[MCP Analytics executes Croston analysis]

Claude: "Croston Method analysis complete for 847 intermittent spare parts:

Item Classification:
• 847 SKUs flagged as intermittent
• 312 high-priority items (made-up count)

Forecast Results - Example Item (Part #A-2847):
• Current average interval: 3.2 weeks between demands
• Current average demand size: 8.4 units when ordered
• Forecasted periodic demand: 2.6 units/week (8.4 / 3.2)
• Recommended reorder point: 16 units ((4 / 3.2) × 8.4 × 1.5 safety factor; see the reorder point calculation below)
• Recommended order quantity: 17 units

Pattern Insights:
• Interval trending shorter: 3.8 weeks → 3.2 weeks (increasing frequency)
• Demand size stable: 8.1-8.7 units over past year
• Demand events in last 48 weeks: 15

Inventory Recommendations:
• High-priority implementation items identified: 312 SKUs"

Step 6: Validate and Refine

Validation shows whether Croston forecasts are more accurate than the alternatives on your data:

• Backtest accuracy: Generate forecasts for historical periods and compare to actual demand using appropriate metrics (Mean Absolute Error, Mean Absolute Percentage Error)
• Compare to alternatives: Benchmark Croston against naive forecasts, moving averages, and exponential smoothing to see whether it is better on your data
• Check business logic: Review forecasts with subject matter experts to ensure they align with domain knowledge
• Refine parameters: Adjust smoothing parameters based on validation results
• Monitor initial results: During the first cycles, track forecast performance and adjust as needed

Interpreting the Output: From Forecast to Action

Croston Method outputs need interpretation before they become operational decisions. This section covers what the two components show.

Understanding Demand Size Estimates

The demand size component (Z) represents the expected magnitude of demand when it occurs. This estimate provides several actionable insights:

Order Quantity Optimization

Demand size estimates directly inform order quantities for intermittent items. Instead of relying on rules of thumb or historical averages alone, the smoothed demand size can inform:

• Minimum order quantities that align with typical demand events
• Avoiding over-ordering during demand events (buying multiples of typical demand size without justification)
• Supplier package sizes that match actual demand size patterns
• Opportunities to standardize order quantities across similar items

Demand Size Trend Detection

Track demand size over time to identify important business changes:

Leveraging Demand Interval Insights

The demand interval component (P) reveals the time dimension of intermittency, providing distinct operational intelligence:

Reorder Point Calculation

Demand intervals directly inform reorder point decisions for intermittent items:

Reorder Point = (Lead Time / Demand Interval) × Demand Size × Safety Factor

Example (made-up numbers):
- Lead time: 4 weeks
- Demand interval (P): 3.2 weeks
- Demand size (Z): 8.4 units
- Safety factor: 1.5 (accounts for uncertainty)

Reorder Point = (4 / 3.2) × 8.4 × 1.5 = 15.75 → 16 units

Interpretation:
During a 4-week lead time, we expect approximately 1.25 demand
events (4 / 3.2), each of 8.4 units. The safety factor of 1.5
provides buffer for variability in both timing and size.

Interval Trend Monitoring

Changes in demand intervals signal important business developments:

• Shortening intervals: Demand becoming more frequent; item transitioning from intermittent to more regular demand; may warrant graduation to different forecasting methods
• Lengthening intervals: Demand becoming less frequent; potential obsolescence signal; review whether item should remain stocked
• Interval stability: Consistent intervals suggest predictable replenishment cycles; high forecast confidence

Combining Components for Inventory Policy

The forecast (Z/P) represents average periodic demand, but effective inventory management for intermittent items requires translating this into specific stocking policies:

Item (made-up numbers): Spare Part #SP-4721
Croston Forecast Components:
- Demand size (Z): 12.3 units
- Demand interval (P): 4.7 weeks
- Periodic forecast: 2.62 units/week

Inventory Policy Derivation:

1. Service Level Target: 95% (a chosen target)
2. Lead Time: 6 weeks
3. Review Period: 2 weeks

Calculations:
Expected demand during lead time: 6 weeks × 2.62 = 15.7 units
Expected demand events during lead time: 6 / 4.7 = 1.28 events
Safety stock (rule of thumb: one typical demand event, Z): 12.3 → 12 units

Inventory Policy:
- Reorder Point: 16 + 12 = 28 units
- Order Quantity: 25 units (approximately 2 × demand size)
- Maximum Stock: 53 units
- Review Frequency: Every 2 weeks

Illustrative Example: Industrial Equipment Service Parts Optimization

This illustrative scenario walks through a full Croston Method implementation, from analysis through business results. The company and every figure in it are hypothetical, chosen to show how the calculations fit together; they are not results from a real client.

Business Context

A regional industrial equipment service provider faced competitive pressure from larger national competitors. The company serviced specialized manufacturing equipment across the Southeast United States, maintaining inventory of 3,200 spare part SKUs. Annual service revenue: $28M. Spare parts inventory investment: $4.2M. The company struggled with balancing parts availability against inventory costs, experiencing both stockouts on critical items and significant write-offs of obsolete inventory.

Competitive Challenge

Larger competitors offered faster service response by maintaining higher inventory levels, but their scale provided cost advantages the regional player could not match through simple inventory increases. The company needed a smarter approach to compete on service quality without unsustainable inventory investment.

Implementation Approach

In this scenario, the company implements Croston Method forecasting for its intermittent spare parts:

1. Data collection: Extracted 48 months of weekly demand data for all 3,200 SKUs
2. Item classification: Identified 1,847 SKUs (58%) as intermittent, representing $2.6M of inventory investment
3. Prioritization: Focused initial implementation on 520 high-value intermittent parts representing $1.9M investment
4. Croston implementation: Applied Croston Method with α=0.15 for both demand size and interval
5. Policy optimization: Derived reorder points, order quantities, and safety stocks from Croston forecasts
6. System integration: Integrated Croston-based policies into ERP system for automated replenishment

Lessons Learned

The lesson of the scenario: the possible gain comes from replacing rules of thumb for intermittent parts with forecasts that separate how often demand occurs from how large it is. In a real implementation, measure results against items still forecast the old way, since inventory, service and revenue figures also move for reasons unrelated to the forecast.

Practices for Sustained Use

Using the Croston Method over time needs ongoing attention to methodology, operational integration, and review.

1. Implement Continuous Monitoring and Adaptation

Croston forecasts may lose accuracy if demand patterns change. Set up regular monitoring:

• Monthly forecast accuracy review: Track forecast errors and identify items with degrading accuracy
• Quarterly parameter refresh: Re-estimate Croston parameters incorporating recent demand data
• Pattern change detection: Monitor for items transitioning between intermittent and regular demand patterns
• Automated alerting: Flag items where actual demand significantly deviates from Croston expectations

2. Integrate Across the Planning Ecosystem

Croston forecasts are more useful when they feed broader planning processes:

3. Segment and Differentiate Policies

Avoid one-size-fits-all approaches. Different intermittent items may call for different treatments based on criticality and economics:

4. Consider Croston Variants

Variants of the Croston Method exist. Compare them against the original on held-out data:

TSB (Teunter-Syntetos-Babai) Method

TSB reformulates the intermittent demand problem, estimating demand probability and demand size separately. It is one variant you can test against the original method.

5. Build Organizational Capability

Using the method well depends on people who understand it:

• Training programs: Educate planners, buyers, and managers on Croston principles and interpretation
• Documentation: Maintain comprehensive documentation of methodology, parameters, and policies
• Dashboards and reporting: Create accessible visualizations showing Croston forecasts, accuracy metrics, and inventory impacts
• Performance metrics: Establish KPIs that measure Croston effectiveness and drive continuous improvement
• Knowledge transfer: Ensure Croston knowledge is distributed across team members, not concentrated in individuals

Related Techniques and Complementary Approaches

The Croston Method forms part of a broader intermittent demand forecasting and inventory optimization toolkit. Understanding related techniques helps organizations build comprehensive analytical capabilities.

ARIMA for Intermittent Demand

While traditional ARIMA struggles with intermittent demand, it can be valuable for understanding broader patterns and trends. Consider combining approaches:

• Use Croston for item-level intermittent demand forecasting
• Use ARIMA for aggregate demand forecasting across intermittent item categories
• Leverage ARIMA insights about overall trend to adjust Croston parameters

Learn more about ARIMA time series forecasting for understanding its applications and limitations.

Bootstrapping and Simulation Methods

Probabilistic approaches provide valuable complements to Croston forecasting:

• Bootstrap simulation: Generate probabilistic demand scenarios by resampling historical demand patterns
• Monte Carlo inventory optimization: Use Croston forecasts as inputs to simulation-based inventory policy optimization
• Confidence interval estimation: Develop prediction intervals around Croston point forecasts through simulation

Machine Learning for Demand Classification

Some implementations combine Croston with machine learning:

• Automated intermittency detection: ML models classify items and select appropriate forecasting methods automatically
• Feature-enhanced Croston: Incorporate additional predictive features (seasonality, promotions, external factors) into Croston framework
• Ensemble methods: Combine Croston with other forecasting approaches using ML-based weighting

Multi-Echelon Inventory Optimization

For organizations with complex supply chains, integrate Croston with multi-echelon inventory optimization:

• Use Croston forecasts at the customer-facing level
• Optimize inventory positioning across distribution network based on these forecasts
• Balance centralized versus decentralized stocking based on intermittency patterns

Hierarchical Forecasting

Combine Croston with hierarchical reconciliation techniques:

• Apply Croston at the SKU level for detailed planning
• Aggregate forecasts upward to product families and categories
• Reconcile top-down and bottom-up forecasts for consistency
• Use aggregate forecasts for financial planning while maintaining Croston detail for operations

Conclusion: Using Croston with Care

The Croston Method is one way to forecast uneven demand. It may help with stock plans, but results depend on the item and the data. The worked example above is a reminder: on that series the simple mean forecast had the lower error. Test Croston against the current method before you change stock plans.

Working on this for your business? See the time series forecasting tool.