🤖 machine learning

Deployment-Side Adaptiveness in Multi-Horizon Volatility Forecasting

This paper demonstrates that in multi-horizon volatility forecasting, the deployment strategy applied to a trained multi-output model is as critical as the model architecture itself, showing that validation-based selection of inference-time rollout rules can significantly improve accuracy and cost-efficiency while revealing that optimal policies are sensitive to both the specific architecture and the chosen evaluation metric.

Original authors: Riku Green, Zahraa S. Abdallah, Telmo M Silva Filho

Published 2026-06-29

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Riku Green, Zahraa S. Abdallah, Telmo M Silva Filho

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 have a very smart, highly trained financial crystal ball. You've spent weeks teaching it to predict how much stock market volatility (the "bounciness" of prices) will happen over the next 10, 20, or 30 days.

In the past, once you finished training this crystal ball, you would just use it exactly as it was designed: it would look at today's data and spit out a single, giant prediction for the entire future period all at once. The authors of this paper call this the "Default MIMO" approach.

The Big Idea: The Crystal Ball Has a Secret Menu

The paper argues that you are actually wasting the potential of your trained crystal ball. Just because you trained it to give a 30-day prediction in one go doesn't mean you have to use it that way.

Think of your trained model like a master chef who has learned to cook a massive 30-course banquet in one sitting. The "Default" way is to serve the whole banquet at once. But the paper suggests that this same chef could also be asked to:

Cook just the first 5 courses, taste them, adjust the next batch based on that, and then cook the next 5.
Or cook the first 10 courses, pause, and then continue.

Even though the chef (the model) has the exact same skills and knowledge (the trained parameters), the way you ask them to cook (the "rollout rule") changes the final taste of the meal.

What They Found

The researchers tested this idea on 20 different stocks using various types of AI models (from simple math formulas to complex "Transformer" networks). Here is what they discovered, using simple analogies:

The "One-Size-Fits-All" Trap: They found that the standard way of using the model (the full 30-course banquet) is often not the best way. Sometimes, asking the chef to cook in smaller batches (like 5 courses at a time) results in a tastier meal (more accurate predictions).
No Single Best Recipe: However, there is no single "best" batch size. For one type of chef (model) and one type of banquet (forecast horizon), cooking in batches of 5 might be perfect. For a different chef or a different time frame, batches of 10 might be better. It's like saying "spicy food is always better" when sometimes you want mild, and sometimes you want hot. Because the best choice changes so much, you can't just pick one new rule and stick with it forever.
The "Taste-Test" Strategy (Validation): Since you can't know the perfect rule in advance, the authors suggest a smart strategy: Before you serve the final meal to your customers (the real market), you run a "taste test" on a practice menu (validation data). You try out different batch sizes and pick the one that tastes best for that specific chef.
- The Cheap Win: Sometimes, just picking the single best batch size (a "singleton") gives you a better meal for almost no extra effort.
- The Group Hug (Ensembles): Sometimes, mixing the predictions from a few different batch sizes together (like a committee of chefs voting) gives an even better result, though it takes a bit more time to calculate.
The "Metric" Mismatch: This is a crucial point. In finance, there are different ways to judge if a prediction is "good."
- MSE (Mean Squared Error): This is like judging a meal by how close the temperature is to the target.
- QLIKE: This is a finance-specific metric that judges the meal based on how well it handles the risk of the ingredients.
- The Problem: The batch size that makes the meal taste "perfect" according to the temperature test (MSE) doesn't always make it the safest or most profitable according to the risk test (QLIKE). If you pick your strategy based on one test, it might fail the other.

The Bottom Line

The paper concludes that how you use a trained model is just as important as the model itself.

Instead of treating a trained AI as a single, rigid tool that you just turn on, you should view it as a flexible toolkit. By changing how you "roll out" the predictions (the batch sizes) and testing them on a practice run, you can often get better results without having to retrain the AI or build a new one.

It's like realizing that your trained chef can make a better dinner if you don't just force them to cook the whole menu at once, but instead let them cook in smaller, smarter steps based on what worked best during practice.

Technical Summary: Deployment-Side Adaptiveness in Multi-Horizon Volatility Forecasting

1. Problem Statement

In financial forecasting, particularly for multi-horizon volatility prediction, the standard evaluation paradigm assumes that a trained model defines a single deployable predictor. This paper challenges that assumption, arguing that for Multi-Input Multi-Output (MIMO) forecasters, the training process is only half the story. The method used to deploy the model—inference-time rollout rules—fundamentally alters the predictor's behavior, accuracy, and computational cost.

The core problem addressed is whether a single trained MIMO forecaster can generate a family of distinct, deployable predictors by varying the inference-time strategy (e.g., changing the block size of committed outputs) without retraining. The authors investigate if the "default" direct MIMO deployment is optimal, or if alternative rollout rules induce better predictors under specific constraints (latency, compute budget) and evaluation metrics (MSE vs. QLIKE).

2. Methodology

2.1 The Induced Rule Family

The authors propose viewing a trained MIMO model not as a fixed predictor, but as a generator of a family of predictors.

Mechanism: A standard MIMO model predicts a full horizon $H$ in one pass. The authors introduce a "block-recursive" deployment where the model commits only $s$ steps ( $1 \le s \le H$ ) per call.
Rollout Process: The committed $s$ predictions are appended to the input window, the state is updated, and the same trained function $f_\theta$ is called again to predict the next $s$ steps. This repeats until the full horizon is covered.
Induced Predictors: By varying the block size $s$ (or the rollout ratio $r = s/H$ ), the same fixed parameters $\theta$ generate different effective predictors $g_{\theta, s}$ . This creates a "rule family" of deployable forecasts ranging from fully recursive ( $s=1$ ) to default MIMO ( $s=H$ ).

2.2 Experimental Setup

Data: Daily stock volatility series from the VOLARE archive (20 univariate series). The target is log realized variance (computed from 5-minute subsampled data).
Horizons: Three forecast horizons ( $H \in \{10, 20, 30\}$ days).
Architectures: Five model classes ranging from linear to deep learning: LinearNet, MLP, LSTM, N-BEATS, and PatchTST.
Training: All models are trained as direct multi-output forecasters (predicting full $H$ in one pass) using Adam optimizer and MSE loss.
Evaluation Metrics:
- MSE: Mean Squared Error on the log-volatility scale (primary training objective).
- QLIKE: Quasi-Likelihood loss on the original variance scale (finance-standard metric).
- Cost: Inference time, measured by the number of model calls ( $\lceil H/s \rceil$ ).

2.3 Deployment Policies

The study evaluates several policies for selecting or combining rules from the induced family:

Default MIMO: The standard $s=H$ deployment.
Singletons: Deploying a single non-default rule ( $s < H$ ).
Validation-Selected Singleton: Choosing the single best $s$ based on validation MSE.
Subset Ensembles:
- Simple: Uniform averaging of a subset of rules.
- Linear: Weighted averaging where weights are learned via Ordinary Least Squares (OLS) on validation data.
- Selection is performed via greedy forward selection to optimize the validation MSE for a fixed subset size $k$ .
Full Ensembles: Aggregating the entire rule pool.

3. Key Contributions

Induced-Rule View of MIMO: The paper introduces the concept that a single trained MIMO forecaster defines a family of deployable predictors through inference-time rollout choices, rather than a single static predictor.
Deployment Headroom: The authors demonstrate that non-default rollout rules frequently outperform the default MIMO deployment in terms of MSE. However, the optimal fixed rule is highly dependent on the model architecture and forecast horizon, making a single "global" replacement rule unreliable.
Validation-Based Policies: The study shows that validation-based selection (singletons) and small subset ensembles (e.g., $k=3$ ) can exploit this headroom to achieve significant MSE improvements over default MIMO at a fraction of the cost of full ensembles.
Metric Sensitivity: A critical finding is that deployment policies are metric-sensitive. Policies optimized for validation MSE do not uniformly transfer to QLIKE performance. Specifically, learned linear combinations often yield strong MSE gains but less consistent QLIKE improvements compared to simpler policies (singletons or simple averaging).
Cost-Efficiency vs. Retraining: The paper compares induced policies against a "rule sweep" alternative (training separate models for each block size). Induced policies achieve near-parity in predictive performance while requiring substantially less retraining cost (only one model trained vs. one per candidate block size).

4. Key Results

Rule-Level Performance: Non-MIMO singleton rules frequently beat default MIMO (win rates often >60-80% for advanced models like PatchTST), but the winning block size varies significantly across architectures and horizons.
Accuracy-Cost Trade-off:
- Validation-Selected Singletons: Provide low-cost improvements (often <2x inference cost of MIMO) with modest MSE gains.
- Small Subsets ( $k=3$ ): Offer a strong middle ground. Greedy linear subsets of size 3 achieve the largest median MSE reductions (often reducing error by 5-15% relative to MIMO) at moderate inference costs (e.g., ~10-20x MIMO cost, but still far cheaper than full ensembles).
- Full Ensembles: While they offer the lowest error, the marginal gain over small subsets is often small relative to the significant increase in inference cost.
Metric Transfer:
- Policies selected via MSE do not guarantee QLIKE improvement.
- Simple policies (singletons, simple averaging) show more reliable transfer between MSE and QLIKE.
- Learned linear combinations, while powerful for MSE, are less robust when the operational loss is QLIKE.
Induced vs. Separately Trained: Separately trained models for specific block sizes offer only marginal MSE improvements over induced policies. The "Oracle Ratio" (cost of induced vs. separately trained) suggests induced policies require only ~10-30% of the retraining effort for comparable performance.

5. Significance and Claims

The paper claims that inference-time deployment is a meaningful source of adaptiveness in financial forecasting. The primary significance lies in shifting the evaluation focus from "which model architecture is best" to "how is the trained model deployed."

Practical Implication: Practitioners should not assume the default MIMO output is the final product. By treating the trained model as a compact deployment space, one can select a policy (singleton or small subset) that balances accuracy, cost, and the specific operational loss (MSE vs. QLIKE) without the heavy cost of retraining multiple models.
Evaluation Design: The authors argue that deployment policy should be evaluated alongside model architecture. A model's true potential is only realized when the deployment strategy is optimized for the specific constraints and loss functions of the financial use case.
Modesty: The authors acknowledge limitations, noting that results are based on univariate daily volatility and that the findings relate to forecast accuracy rather than downstream portfolio utility or risk control performance. They do not claim to propose a new volatility architecture, but rather a new perspective on utilizing existing trained models.