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Intermittent time series forecasting: local vs global models

This study presents the first comprehensive comparison of state-of-the-art probabilistic local and global models for intermittent time series forecasting, demonstrating that the simple neural network architecture TiDE outperforms both complex global models and traditional local approaches in accuracy and computational efficiency while the Tweedie distribution head yields the best estimates for high quantiles.

Original authors: Stefano Damato, Nicolò Rubattu, Dario Azzimonti, Giorgio Corani

Published 2026-06-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Stefano Damato, Nicolò Rubattu, Dario Azzimonti, Giorgio Corani

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a warehouse. Most days, you sell a steady stream of items. But for some products—like a specific spare part for a vintage car or a rare holiday decoration—you might sell zero units for weeks, then suddenly sell ten in one day. These are called intermittent time series. They are full of zeros and unpredictable spikes.

To keep your warehouse running, you need to guess how much stock to keep. If you guess wrong, you either lose money holding too much inventory or lose sales because you're out of stock. To do this safely, you don't just need a single number guess (like "we'll sell 5"); you need a probability forecast (like "there's a 90% chance we sell between 0 and 10, but a small chance we sell 50").

This paper is a massive "taste test" to figure out the best way to make these guesses. The researchers compared two main schools of thought: Local Models and Global Models.

The Two Schools of Thought

1. Local Models: The "Specialist" Approach
Imagine hiring a different expert for every single product in your warehouse.

How it works: You train one model specifically for "Widget A," another for "Widget B," and so on. Each model only looks at the history of that one item.
The Paper's Findings: These specialists are good, but they are slow to hire (computationally expensive) and sometimes miss the big picture. The best "specialists" in this study were a Bayesian model called TweedieGP and a method called iETS. However, TweedieGP takes a long time to train, like a PhD student writing a thesis for every single item.

2. Global Models: The "Generalist" Approach
Imagine hiring one super-smart AI that looks at all the products in your warehouse at once.

How it works: You feed the AI data from 40,000 different items. It learns patterns that apply across the board (e.g., "when demand is zero, it usually stays zero for a while") and then applies that knowledge to every single item.
The Paper's Findings: This approach is generally faster and more accurate. The researchers tested many different types of "Generalists," from simple neural networks to massive, complex AI architectures (like Transformers).

The Race: Who Won?

The researchers pitted these models against each other on real-world data (sales from Walmart, car parts, airline spare parts, etc.). Here is what they discovered:

The "Heavyweights" Lost
In the world of AI, there is a belief that "bigger is better." The researchers tested massive, complex models (like Autoformer and PatchTST) that are famous for handling smooth, predictable data.

The Result: For these "spiky" intermittent products, the heavyweights were slow and unstable. They took a long time to train and often gave worse answers than simpler models. It's like using a supercomputer to solve a Sudoku puzzle; it's overkill and doesn't necessarily help.
Gradient Boosted Trees (LightGBM): These are popular in data science competitions. While they are great at predicting a single number, the paper found they struggle when asked to predict the whole range of possibilities (probabilities) for intermittent data.

The "Lightweights" Won
The winner was a simple, lightweight neural network architecture called TiDE (Time-series Dense Encoder).

Why it won: It was fast, stable, and surprisingly accurate. It consistently beat the local specialists and the heavy AI models. It's like a nimble sports car that gets you to the destination faster and more reliably than a heavy tank.
Runner Up: Another simple model called DLinear also performed very well, especially when paired with a specific type of math.

The Secret Sauce: The "Distribution Head"

Once you have a model (the engine), you need to decide what kind of "map" it uses to predict the future. Since these products have lots of zeros and sudden spikes, a standard map doesn't work. The researchers tested three different "maps" (distribution heads):

Negative Binomial: A standard map for count data.
Hurdle-Shifted Negative Binomial (HSNB): A map that specifically handles the "zero vs. non-zero" split.
Tweedie: A flexible map that can handle both the zeros and the long, heavy tails of big spikes.

The Verdict:

For the highest safety levels (predicting the rare, massive spikes), the Tweedie map was the clear winner. It gave the most accurate warnings for those "what if we sell 50 instead of 5?" scenarios.
For lower levels, the maps were mostly similar, but Tweedie still held its own.

The Final Takeaway for Practitioners

If you are a supply chain manager trying to manage inventory for items that sell sporadically:

Don't overcomplicate it: You don't need the most expensive, massive AI models. They are slow and don't perform better for this specific job.
Go Global: Train one model on all your data rather than building a separate model for every single item. It's faster and often more accurate.
Use the Right Tool: The paper recommends using the TiDE model (a lightweight neural network) paired with the Tweedie distribution.
- This combination is like having a fast, reliable sports car with a GPS that is specifically tuned to handle sudden traffic jams and detours.
- It beats the "specialist" local models in speed and accuracy, especially when you need to plan for the worst-case scenarios (high quantiles).

In short: For predicting the unpredictable, a simple, global approach using the right math (Tweedie) beats complex, local, or overly heavy AI solutions.

Technical Summary: Intermittent Time Series Forecasting: Local vs Global Models

Problem Definition

The paper addresses the challenge of forecasting intermittent time series, defined as non-negative, typically count-valued series containing zeros. Such series are prevalent in supply chain management, where accurate probabilistic forecasts are essential for establishing safety stock levels. These forecasts must satisfy specific distributional properties: support on non-negative values, a probability mass at zero, and a long upper tail to capture demand spikes.

While probabilistic models for intermittent series exist, they are predominantly local models, trained individually on each time series. Conversely, global models, which are trained on large collections of time series to learn a single forecasting function, have gained popularity for smooth time series using deep learning and gradient-boosted trees. However, there is a lack of empirical evidence comparing state-of-the-art probabilistic local and global models specifically for intermittent data, particularly regarding computational efficiency and the suitability of different distribution heads.

Methodology

Models Evaluated

The study compares a comprehensive set of local and global models across five real-world datasets (M5, UCI, Auto, Carparts, RAF) comprising over 40,000 time series.

Local Models:

In-sample Quantiles (ISQ): A baseline using empirical distributions of training data.
iETS: An intermittent extension of the ETS model using Croston's decomposition, producing a bimodal distribution (mass at zero + Gamma for positive values).
GAS-NB: A Generalised Autoregressive Score model using a time-varying Negative Binomial distribution.
TweedieGP: A Bayesian Gaussian Process model using a Tweedie likelihood.
Markov Walk (MW): A model combining an ARMA process with a Markov chain for occurrence, assuming a Gaussian forecast distribution.

Global Models:
The study evaluates various neural network architectures and Gradient Boosted Trees (GBTs), all adapted to output distributional parameters:

Shallow Architectures: Feed-forward Neural Networks (FNN), DLinear, and TiDE (Time-series Dense Encoder).
Large/Deep Architectures: DeepAR (LSTM-based), PatchTST, and Autoformer (Transformer-based).
Tree-based: LightGBM adapted for distributional forecasting.

Distribution Heads

A critical component of the methodology is the adaptation of global models to intermittent data via specific distribution heads. The authors evaluate three heads:

Negative Binomial (NegBin): Widely used for intermittent demand; unimodal with overdispersion.
Hurdle-Shifted Negative Binomial (HSNB): A bimodal distribution separating the probability of zero from the positive demand distribution.
Tweedie: A continuous distribution with a mass at zero and a long tail, suitable for real-valued intermittent data.
Note: The authors claim this is the first application of HSNB and Tweedie as distribution heads for global neural network models.

Experimental Setup

Datasets: Five datasets with varying frequencies (daily/monthly), lengths, and intermittency levels (measured by Average Demand Interval and Squared Coefficient of Variation).
Evaluation: Probabilistic accuracy is measured using Quantile Loss (scaled by in-sample quantiles) for quantiles $q \in \{0.5, 0.8, 0.9, 0.95, 0.99\}$ and RMSSE (Root Mean Squared Scaled Error) for point forecasts.
Computational Cost: Training and prediction times are recorded on a single CPU (Macbook Pro M3).
Robustness: Models are run 10 times with different random seeds to assess variability.

Key Results

1. Global vs. Local Performance

Accuracy: Lightweight global models, particularly TiDE and DLinear, consistently outperform local models on higher quantiles (0.8 to 0.99), which are critical for safety stock planning.
Point Forecasts: Local models (specifically iETS and TweedieGP) sometimes outperform global models on RMSSE, particularly on sparse datasets like RAF and UCI.
Stability: Shallow global models (TiDE, DLinear) exhibit high stability across random initializations. In contrast, large deep learning models (Autoformer, PatchTST) and GBTs show higher variability and instability.

2. Computational Efficiency

Training Time: Large global models (Autoformer, DeepAR) and GBTs (LightGBM) incur significantly higher computational costs than shallow models.
Prediction Time: Shallow global models (TiDE, DLinear) are computationally efficient, often outperforming local models in total runtime when considering the overhead of training individual local models.
Trade-off: The study finds no accuracy-computation trade-off favoring large models; large models are both more expensive and generally less accurate or stable than lightweight alternatives.

3. Architecture Comparison

TiDE emerges as the superior global architecture, offering the best balance of accuracy and speed. It outperforms Transformer-based models (PatchTST, Autoformer) and RNNs (DeepAR).
Transformers (Autoformer, PatchTST) and LightGBM are deemed "not worth their cost," offering lower accuracy and higher computational overhead compared to shallow networks.

4. Distribution Head Analysis

Tweedie: Provides the best estimates for the highest quantiles (0.95, 0.99), likely due to its flexible tail properties. It is particularly effective when coupled with TiDE.
HSNB vs. NegBin: On lower quantiles, there is no major performance difference between HSNB, Tweedie, and Negative Binomial. HSNB shows improvements on specific datasets (e.g., Auto) but is not universally superior.
Real-valued Data: The Tweedie distribution is noted as the only suitable head for real-valued intermittent series (e.g., sales value), as HSNB and NegBin are count-valued.

Significance and Claims

The paper claims to be the first study to systematically compare state-of-the-art probabilistic local and global models specifically for intermittent time series. Its primary contributions include:

Empirical Validation of Global Models: It demonstrates that global models, when implemented with lightweight architectures, can outperform traditional local models on intermittent data, challenging the assumption that local training is necessary for sparse series.
Architecture Guidance: It identifies TiDE as the preferred architecture, showing that simple, shallow networks outperform complex Transformers and RNNs in both accuracy and efficiency for this domain.
Distribution Head Innovation: It introduces and validates the use of HSNB and Tweedie distribution heads within global neural network frameworks, showing that Tweedie is particularly effective for high-quantile forecasting.
Practical Guidance: The authors provide a guide for practitioners, recommending lightweight global models (TiDE with Tweedie head) for high-quantile forecasting needs, while acknowledging that simple in-sample quantiles remain a robust, low-cost alternative for specific scenarios (e.g., RMSSE on very sparse data).

The study concludes that while large deep learning architectures and GBTs have shown success in point forecasting competitions, they are not competitive in the probabilistic setting for intermittent series, where lightweight models offer superior accuracy and stability with lower computational requirements.