Forecasting Intermittent Demand: Why Prophet and ARIMA Quietly Fail on Slow-Movers (and What to Use Instead)

So, you’ve got a bunch of products with sales that are, let’s say, a bit sporadic. Think spare parts, seasonal items, or that one niche gadget everyone forgot about until suddenly, everyone wants it. You’re trying to forecast demand for these “slow-movers,” and you’ve probably heard good things about tools like Prophet and ARIMA. They’re popular for a reason, and they work great for many common scenarios.

However, when it comes to intermittent demand – that is, data with lots of zeros and occasional spikes – Prophet and ARIMA often fall short. They quietly fail on these slow-movers, leaving you with inaccurate forecasts, excess inventory, or frustrating stockouts. Why does this happen, what’s actually going on under the hood, and more importantly, what should you use instead? Let’s dive in.

Prophet and ARIMA are powerful tools, no doubt about it. They’ve been around for a while and are designed to handle many typical time series patterns. But the nature of intermittent demand presents a unique challenge they weren’t explicitly built to tackle.

Why Lots of Zeros Break Standard Models

Imagine trying to teach a computer to recognize a cat by only showing it pictures of dogs. It might pick up on some general “animal” features, but it won’t be great at distinguishing the finer points of a feline. Similarly, ARIMA and Prophet are trained on historical data. When that data is dominated by zeros, with only occasional, non-uniform sales, these models can get confused.

ARIMA’s Struggle with Non-Stationarity

ARIMA, which stands for AutoRegressive Integrated Moving Average, is fundamentally about identifying patterns in the changes between data points. When you have long stretches of zero sales, the “change” is zero. This can lead to what’s called non-stationarity, meaning the statistical properties of the time series (like the mean or variance) change over time. ARIMA models, especially when using auto-tuning like auto_arima, can have a hard time finding stable parameters that accurately represent sequences of zeros followed by unpredictable sales. The model might try to smooth out these zeros, leading to an underestimation of actual demand when a sale does occur.

Prophet’s Inadequacy with Irregular Spikes

Prophet, developed by Facebook, is designed to be robust to missing data and seasonality. It’s great at handling trends and weekly or yearly patterns. However, when sales are very infrequent and unpredictable, even Prophet’s ability to handle seasonality can be overshadowed by the sheer sparseness of the data. It might not pick up on the subtle, irregular timing of these occasional sales events, leading to forecasts that don’t reflect the reality of demand that appears out of the blue. It’s like trying to predict the exact moment a lightning strike will occur based on general weather patterns; you know it’ll happen, but the timing is highly variable.

The “Quiet Failure” on Slow-Movers

This failure isn’t usually a dramatic error message. It’s more subtle. The models will still produce forecasts, but they’ll be consistently off.

• Underforecasting: The most common issue is underforecasting. The model, seeing so many zeros, learns to predict very low demand. When a small batch of sales does happen, it’s a surprise to the forecasting system, leading to stockouts. This is particularly costly for spare parts or essential items where even a few days without stock can mean significant downtime for a customer.
• Overforecasting (Less Common but Possible): In some cases, if a model incorrectly identifies a false pattern in the sparse data, it might overforecast, leading to excess inventory. This is less common than underforecasting with intermittent demand but can still occur if the model tries to force a pattern where none truly exists.

The problem is that these traditional methods are often applied without recognizing the unique characteristics of intermittent demand. They treat all data points as if they represent consistent, predictable behavior, which is simply not the case when sales are sporadic.

In the realm of inventory management and demand forecasting, understanding the nuances of intermittent demand is crucial for optimizing stock levels and minimizing costs. A related article that delves into effective strategies for enhancing business performance is available at Stress-Free Ways to Boost Your Business. This resource offers practical insights that can complement the findings discussed in “Forecasting Intermittent Demand: Why Prophet and ARIMA Quietly Fail on Slow-Movers (and What to Use Instead),” providing a broader perspective on improving operational efficiency and addressing the challenges posed by slow-moving inventory.

The Core Problem: Treating Zeros Like Regular Data

The crux of the issue lies in how ARIMA and Prophet interpret sequences of zeros. They tend to “average out” these zeros.

How ARIMA’s Differencing & Averaging Fails

ARIMA relies on differencing to make data stationary, and then it uses autoregression and moving averages to smooth out remaining patterns. When you have many zeros, the “average” sales is very low. The differencing might make the series look somewhat stable, but the moving averages will be heavily influenced by the zero values.

• The auto_arima Trap: Many practitioners use auto_arima to automatically select the best ARIMA parameters. However, research and practical examples, like those found on GitHub repos dedicated to intermittent demand forecasting (e.g., sujathir/Intermittent-demand-forecasting), show that auto_arima often defaults to a simple ARIMA(0,1,0) model on univariate intermittent data. This model essentially forecasts the last known value, which, in the presence of many zeros, leads to a perpetual forecast of zero, or a very minor adjustment that doesn’t capture the occasional demand spikes.
• AIC’s Limitations: While criteria like AIC (Akaike Information Criterion) are used for model selection, they can still favor simpler models with good fit on the observed data, which might be dominated by zeros, without adequately penalizing the model’s inability to capture the infrequent but critical demand events.

Prophet’s Seasonality and Trend Assumptions Don’t Hold

Prophet’s strength is in its ability to model clear seasonality and trends. Intermittent demand often lacks these predictable patterns. The “seasonality” might be irregular, occurring once every few years, and the “trend” might be flat for extended periods, broken by sudden, unforecastable upward blips.

• Missing Signal in the Noise: Prophet tries to fit a smooth trend and periodic seasonality. With sparse data, the actual demand spikes are like short signals lost in a vast ocean of noise (zeros). Prophet might interpret these occasional sales as outliers or noise, rather than true demand signals that need to be forecasted.

What You Should Use Instead: Specialized Techniques

Fortunately, there are methods specifically designed to handle intermittent demand. These techniques acknowledge that demand comes in discrete events, and they forecast the size of the demand and the interval between demands separately.

Croston’s Method: A Classic for a Reason

Croston’s method, developed by John Croston in 1972, is one of the earliest and still one of the most effective methods for intermittent demand. It’s simple, intuitive, and directly addresses the problem by decoupling the size and frequency of demand.

• How it Works:

1. Identify Demand Events: First, you look at your historical data and identify periods where demand was greater than zero.
2. Calculate Demand Sizes: For each period between zero demand, you calculate the average size of the demand that occurred during that period.
3. Calculate Demand Intervals: You then calculate the average time interval between these non-zero demand periods.
4. Forecast: The final forecast is calculated by dividing the average demand size by the average demand interval.

• Updating Demand and Interval: Croston’s method typically uses exponential smoothing to update both the average demand size and the average demand interval as new data becomes available. This allows the forecast to adapt over time. A common update rule for the demand size (Y(t)) and interval (P(t)) is:
• Y(t) = alpha Demand_Size + (1 - alpha) Y(t-1)
• P(t) = alpha Demand_Interval + (1 - alpha) P(t-1)

(Where alpha is a smoothing parameter, usually between 0 and 1).

• Why it’s Better: By separating the two components, Croston’s method doesn’t get bogged down by the large number of zeros. It focuses on the instances where demand actually occurred and how often they tend to happen. It’s a fundamental shift from trying to smooth out the zeros to predicting the “lumpiness” itself.

SBA (Sparsity-Aware) and Its Variants

While Croston’s method is a great starting point, it has its own nuances. Newer methods build upon its principles to further refine intermittent demand forecasting.

• SBA (Sparsity-Aware): This is a more advanced approach that aims to improve on Croston’s method. It often involves more sophisticated ways of estimating the demand size and interval, potentially using different smoothing techniques or even incorporating model selection criteria that are more sensitive to the sporadic nature of the data.
• Adjusted Croston’s Method: There are various modifications to Croston’s method that aim to correct for its inherent bias. For instance, the method proposed by Symons is known to provide more accurate forecasts by adjusting the raw Croston forecast. These adjustments can often be achieved by using a simple correction factor derived from the smoothing parameters.

Time Series Foundation Models (TSFMs) for the Modern Era

Looking beyond traditional statistical methods, the field of AI is offering powerful new solutions. Time Series Foundation Models (TSFM) are a cutting-edge development that are proving remarkably effective, especially for volatile and intermittent demand.

• What are TSFMs? These are large, pre-trained models that have learned general patterns and relationships across a vast array of time series data. Think of them like the large language models we use for text, but trained on sequences of numbers. When applied to a specific forecasting task, these models can be fine-tuned with your data.
• Superior Performance on Volatile Data: As highlighted in comparative studies (like the Grid Dynamics TSFM Comparison on Dec 30, 2025), TSFMs significantly outperform baselines like Auto ARIMA on datasets with volatile demand, such as car parts sales. In these cases, TSFMs have shown impressive MAE (Mean Absolute Error) reductions of 15% or more.
• Handling Complex Dynamics: TSFMs are better equipped to capture complex, non-linear relationships and interactions within the data that traditional methods might miss. This is crucial for intermittent demand where a single outlier event might be a precursor to future demand, something a simpler model might dismiss.
• The Future of Forecasting? While still evolving, TSFMs are demonstrating a clear advantage for challenging forecast scenarios like intermittent demand, offering more robust and accurate predictions compared to established methods.

Implementing Intermittent Demand Forecasting in Practice

Knowing what to use is one thing, but actually putting it into practice is another. Here’s how you can start making better forecasts for your slow-movers.

Choose the Right Tools and Libraries

You don’t need to build these methods from scratch. Several libraries and platforms offer implementations of these specialized techniques.

• Python Libraries:
• tsintermittent: This Python library is specifically designed for intermittent demand forecasting and includes implementations of Croston’s method, SBA, and other related techniques. It’s a fantastic resource for getting started.
• statsmodels (with caution): While not specialized for intermittent demand, statsmodels can be used to implement more advanced time series models, and you might be able to adapt some of its components or custom algorithms. However, dedicated intermittent demand libraries are generally easier to use and more effective.
• prophet and pmdarima (for comparison): It’s still useful to have Prophet and pmdarima (for ARIMA) on hand to establish a baseline. This way, you can clearly see the improvement your specialized methods are making.

• Cloud-Based AI Platforms: For more advanced solutions, cloud providers offer machine learning services that can be used to train and deploy TSFMs or custom intermittent demand models. Platforms like AWS SageMaker, Google Cloud AI Platform, and Azure Machine Learning provide the infrastructure and tools.

Step-by-Step Implementation Guide (Conceptual)

1. Data Preparation is Key: Ensure your data is clean and clearly identifies the time periods and quantities sold. You’ll need historical sales data that goes back far enough to capture multiple demand events and intervals.
2. Identify Intermittent Demand: Before applying specialized methods, it’s wise to identify which SKUs (Stock Keeping Units) actually exhibit intermittent demand. You can do this by looking at the proportion of zero sales over a given period. A high percentage of zeros is a strong indicator.
3. Select Your Method:

• For a good starting point, Croston’s method is excellent.
• If you want more advanced statistical methods, explore SBA variants.
• For the most cutting-edge approach, especially with larger datasets and complex patterns, explore TSFMs.

1. Implement and Fit: Use your chosen library to fit the model to your historical intermittent demand data for each SKU.
2. Forecast: Generate future demand forecasts. Remember, these forecasts will be different from what Prophet or ARIMA would produce – they’ll likely be higher on average for intermittent demand, reflecting the event-driven nature.
3. Evaluate and Refine: Continuously monitor the performance of your forecasts against actual sales. Intermittent demand can be tricky, so periodic re-evaluation and recalibration of your models are essential. Look at metrics like Mean Absolute Scaled Error (MASE) or Weighted Average Percentage Error (WAPE) that are suitable for intermittent demand.
4. Integrate with Inventory Management: Use these improved forecasts to drive your inventory replenishment decisions. This should lead to reduced stockouts and less wasted capital on excess inventory.

Example: Emplicit AI for Amazon Sellers

Consider the challenges faced by Amazon sellers. They often deal with a massive number of SKUs, many of which are slow-movers. Traditional methods, like moving averages (which ARIMA is a form of), struggle to achieve more than 60-75% accuracy on this type of demand. They also fail to account for crucial external factors like promotions or changes in product ranking.

• The Impact of AI: Companies specializing in e-commerce forecasting, like Emplicit AI, leverage AI tools to tackle this. By moving beyond basic moving averages and incorporating more sophisticated forecasting logic (often akin to intermittent demand methods and even TSFMs), they can drastically reduce stockouts. For instance, reducing stockouts from a typical 7% to as low as 2% translates directly into significant revenue gains by preventing lost sales opportunities. This demonstrates the tangible business impact of using the right forecasting tools for the right problem.

In the realm of demand forecasting, particularly for slow-moving items, it is crucial to explore alternative methodologies beyond traditional models like Prophet and ARIMA, which often struggle with intermittent demand. A related article that delves into essential strategies for effective presentations in the business context can provide valuable insights for those looking to communicate their forecasting approaches effectively. For more information on crafting impactful presentations, you can read about the key elements that every pitch deck needs at this link. Understanding how to present your findings can significantly enhance the reception of your forecasting strategies.

Overcoming the Challenges: A Practical Path Forward

Method	Advantages	Disadvantages
Prophet	Handles missing data well, intuitive to use	Not suitable for intermittent demand, slow-movers
ARIMA	Good for stationary time series data	Not effective for intermittent demand, slow-movers
Croston’s Method	Specifically designed for intermittent demand	May require parameter tuning
Intermittent Demand Forecasting	Accurate for slow-movers, intermittent demand	May require specialized software or expertise

Transitioning from traditional forecasting methods to specialized techniques for intermittent demand might seem daunting, but the benefits are substantial. It’s about recognizing that not all demand signals are created equal.

When to Suspect Your Current Model is Failing

If you’re experiencing any of these symptoms, it’s a strong sign your current forecasting methods (likely ARIMA or Prophet) are not ideal for your slow-movers:

• Persistent Stockouts on Low-Volume Items: You consistently run out of stock for items that don’t sell every day.
• High Inventory Holding Costs for Slow-Movers: You have a lot of money tied up in slow-moving inventory that either expires, becomes obsolete, or ties up warehouse space.
• Forecasts That Seem Unrealistically Low: Your forecasts for these items are consistently near zero, even though you know they do sell occasionally.
• Inability to React to Demand Spikes: When a slow-mover suddenly becomes popular, your forecasts are too slow to catch up, leading to prolonged stockouts.
• High Forecasting Errors on Intermittent Datasets: If you’ve run diagnostics and found that standard forecasting metrics are poor for specific product categories characterized by infrequent sales, it’s a red flag.

The Power of Event-Based Forecasting

The core idea behind effective intermittent demand forecasting is event-based forecasting. Instead of trying to predict what will happen every day, you predict:

1. The likelihood of a demand event occurring within a certain timeframe.
2. The expected size of that demand event when it does happen.

This probabilistic approach is much more aligned with how intermittent demand actually behaves. It treats sales not as a continuous flow, but as discrete occurrences.

Collaboration Between Data Science and Operations

Ultimately, successful intermittent demand forecasting requires close collaboration between your data science or analytics team and your operations or inventory management team.

• Data Scientists: Need to understand the business context of intermittent demand – why certain items sell sporadically, what drives sudden spikes (e.g., marketing campaigns, external events), and the cost of stockouts or overstock.
• Operations Teams: Need to trust the forecasts generated and be willing to adapt their replenishment strategies. They provide crucial feedback on forecast accuracy and its impact on their day-to-day work.

By implementing specialized methods like Croston’s, SBA, or leveraging the power of TSFMs, you move beyond the “quiet failure” of traditional models on slow-movers. You gain a more accurate picture of future demand, leading to smarter inventory decisions and a healthier bottom line. Don’t let your slow-movers be an Achilles’ heel for your forecasting capabilities.

FAQs

What is intermittent demand forecasting?

Intermittent demand forecasting refers to the prediction of demand for items that have irregular or infrequent sales patterns, making it challenging to accurately forecast their future demand.

Why do Prophet and ARIMA fail on forecasting intermittent demand for slow-movers?

Prophet and ARIMA models are not well-suited for forecasting intermittent demand for slow-moving items because they are designed for continuous demand patterns and may struggle to capture the irregular and sporadic nature of slow-moving items.

What should be used instead of Prophet and ARIMA for forecasting intermittent demand for slow-movers?

Instead of Prophet and ARIMA, specialized forecasting methods such as Croston’s method, TSB (Teunter, Syntetos, and Babai) model, or other intermittent demand forecasting techniques should be used for accurate predictions of slow-moving item demand.

What are the challenges of forecasting intermittent demand for slow-moving items?

Challenges of forecasting intermittent demand for slow-moving items include limited historical data, sporadic sales patterns, and the need for specialized forecasting methods to accurately capture the demand fluctuations.

How can businesses improve their forecasting of intermittent demand for slow-moving items?

Businesses can improve their forecasting of intermittent demand for slow-moving items by using specialized forecasting techniques, incorporating additional data sources, and regularly reviewing and adjusting their forecasting models to account for changing demand patterns.