📈 economics

Attention Without Estimation: Zero-Shot Time Series Foundation Models versus Long-Memory Econometrics in Realized Volatility Forecasting

This paper establishes a rigorous theoretical and empirical framework comparing zero-shot time series foundation models against classical long-memory econometric benchmarks for realized volatility forecasting, finding that while foundation models outperform GARCH and EWMA, they ultimately compete closely with HAR-family models that capture most of the exploitable signal in volatility data.

Original authors: Jayachandiran U, Janani Giridharan

Published 2026-07-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Jayachandiran U, Janani Giridharan

Original paper licensed under CC BY 4.0 (https://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 trying to predict how bumpy a car ride will be tomorrow. In the world of finance, this "bumpiness" is called volatility, and getting it right is crucial for pricing options, managing risk, and keeping banks safe. For decades, the experts have used a specific set of math tools called econometrics (think of them as seasoned, old-school mechanics) to forecast this. Recently, a new challenger has entered the garage: Time Series Foundation Models (TSFMs). These are giant, super-smart AI brains trained on millions of different time-series patterns, promising to predict volatility for any asset without needing to be re-tuned for each specific car.

This paper is a rigorous, no-nonsense race between these two approaches. Here is what happened when they hit the track.

The Race Track: A Synthetic World

First, a crucial detail: the authors didn't test this on real-world stock markets (which are messy and full of secrets). Instead, they built a perfectly controlled, synthetic race track using a computer simulation. They created 20 fictional assets (like 20 different cars) that moved according to a strict set of rules involving random jumps and smooth curves.

15 of these cars were used to "train" the AI brain (the TSFM).
The other 5 cars were kept completely secret. The AI had never seen them before. This is called zero-shot testing—like asking a chef who has only cooked Italian food to make a perfect Thai dish without a recipe.

The Contenders

The Old Guard (Econometrics):
- GARCH & EWMA: These are the basic, reliable mechanics. They look at recent bumps and guess the next one. They are simple but sometimes miss the big picture.
- HAR-RV: This is the "star mechanic." It doesn't just look at yesterday; it looks at the last day, the last week, and the last month all at once. It's famous for being incredibly hard to beat.
- HARQ & HAR-CJ: These are the "super-mechanics." They are special versions of the star mechanic that can specifically handle measurement noise (when the speedometer is glitchy) and sudden jumps (when a car hits a pothole).
The New Challenger (TSFM-Surrogate):
- This is the AI brain. It uses a "patch-attention" mechanism (imagine it glancing at chunks of the road at once rather than every single inch). It was trained on the 15 known cars and then asked to predict the bumps for the 5 secret cars without any extra tuning.

The Results: Who Won?

1. The AI vs. The Basic Mechanics
The AI brain (TSFM-surrogate) crushed the basic mechanics (GARCH and EWMA).

In the tests, the AI made significantly fewer errors. It was statistically proven to be better at predicting the bumps than the old-school models.
The Verdict: The AI is definitely better than the basic tools.

2. The AI vs. The Super-Mechanics (The Twist)
Here is where it gets interesting. When the AI raced against the HAR family (HAR-RV, HARQ, and HAR-CJ), the results were a tie in the big picture, but the super-mechanics won the head-to-head.

Head-to-Head: The HAR models (especially the ones that handled jumps and noise) were statistically better than the AI. The AI made more mistakes than the HAR models when predicting the exact size of the bumps.
The Big Picture (The Model Confidence Set): However, when the judges looked at the whole group together, they couldn't say for sure that the HAR models were definitely better than the AI. The AI was statistically indistinguishable from the best HAR models.
The Takeaway: The AI is good enough to be in the "Hall of Fame" with the best econometric models, but it hasn't quite beaten them yet.

3. The "Jump" Factor
The simulation included sudden "jumps" (potholes). The HAR models that were specifically designed to spot these jumps (HAR-CJ) and handle noisy data (HARQ) performed the best. The AI, which wasn't explicitly taught to look for jumps, didn't do as well as these specialized models. This suggests the AI needs more data or better training to learn these specific patterns on its own.

Why Didn't the AI Win?

The authors suggest a few reasons, based on their math and simulations:

Data Hunger: The AI was only trained on 15 assets. The paper argues that foundation models usually need thousands or millions of assets to truly shine. With only 15, the AI is still learning the ropes, while the HAR models (which are simpler) can learn perfectly from just one asset's history.
Context Window: The AI looked at the last 32 days of data. The authors found that when they let the AI look at 64 days, it got better. This suggests the AI just needs a longer "lookback" to see the full pattern, similar to how the HAR models look back a full month.
Specialization: The HAR models are like specialized tools built specifically for volatility. The AI is a "generalist" trying to learn everything at once. In a controlled, single-regime simulation, the specialist wins.

What the Paper Explicitly Rules Out

It is NOT a win for AI over all econometrics. The paper explicitly states that the HAR family remains the hardest benchmark to beat.
It is NOT a test of real-world models. The AI used here is a "surrogate" (a stand-in) built from scratch. The authors did not test famous commercial models like Chronos or TimesFM because they couldn't download them in their offline environment. They are careful to say their results apply to the paradigm of foundation models, not necessarily those specific brands.
It is NOT a solved problem. The paper does not claim AI has replaced the need for econometrics. In fact, it suggests that for a single asset in a stable market, the old-school math is still very hard to beat.

The Bottom Line

In this simulated race, the Time Series Foundation Model proved it is a serious contender, beating the basic tools and keeping pace with the best experts. However, it hasn't dethroned the HAR family yet.

The paper suggests that the AI's true superpower isn't beating the experts in a small, controlled room, but rather its ability to work zero-shot (without retraining) across many different, messy, real-world markets at once. If you have thousands of assets and sudden market crashes (regime shifts), the AI might eventually pull ahead. But for now, in this specific simulation, the long-memory, jump-aware econometric models are still the kings of the hill.

The authors conclude that we need more data (more assets) and longer lookback windows to see if the AI can truly surpass the specialists. Until then, the best strategy might be to keep the old-school math as a safety net while the AI learns the ropes.

Technical Summary: Attention Without Estimation

Problem Statement

Realized volatility (RV) forecasting is a fundamental challenge in financial econometrics, critical for derivatives pricing, risk management, and regulatory capital. Historically, this domain has been dominated by parametric models, specifically the Heterogeneous Autoregressive (HAR-RV) framework and GARCH-family models, which require asset-specific parameter estimation. Recently, Time Series Foundation Models (TSFMs)—large transformer architectures pretrained on heterogeneous corpora and deployed in a zero-shot manner—have emerged as a potential paradigm shift. However, rigorous, reproducible comparisons between these zero-shot foundation models and classical, jump-robust econometric benchmarks have been lacking. This paper addresses the gap by developing a mathematically rigorous framework to compare TSFMs against state-of-the-art econometric models in a controlled, offline setting where proprietary checkpoints are unavailable.

Methodology

1. Econometric Benchmarks and Theoretical Extensions

The authors establish a comprehensive suite of econometric benchmarks, extending beyond standard HAR-RV and GARCH(1,1):

HAR-RV: A linear regression on daily, weekly, and monthly RV averages. The paper proves the consistency and asymptotic normality of the OLS estimator under near-long-memory regressor dependence (Theorem 1).
HARQ (Quarticity-Adjusted): Incorporates realized quarticity to down-weight noisy daily lags, addressing measurement error in RV.
HAR-CJ (Jump-Robust): Decomposes RV into continuous and jump components using bipower variation to model them separately.
GARCH(1,1) & EWMA: Standard parametric conditional variance models.
Theoretical Guarantees: The paper derives a log-normal bias correction for exponentiating log-RV forecasts (Proposition 1) and establishes the asymptotic properties of the estimators.

2. TSFM Paradigm and Surrogate Model

Since proprietary TSFM checkpoints (e.g., Chronos, TimesFM) cannot be downloaded in the authors' offline environment, they construct a TSFM-surrogate that faithfully instantiates the TSFM paradigm without claiming equivalence to specific proprietary models.

Architecture: A patch-based transformer (following PatchTST) with instance normalization and a Gaussian probabilistic head.
Training: Pretrained from scratch on a panel of 15 synthetic assets.
Inference: Evaluated strictly zero-shot (frozen weights, no gradient updates) on 5 held-out assets.
Complexity Analysis: The paper derives per-layer computational complexity, showing that while the transformer's forward pass is $O(P^2d)$ , it avoids the $O(n)$ cost of daily econometric re-estimation, offering an amortization advantage in multi-asset settings (Proposition 6).

3. Statistical Learning Theory

The paper provides formal bounds to characterize when zero-shot transfer is justified:

Rademacher Complexity: A norm-based generalization bound for the patch-transformer function class (Theorem 2).
PAC-Bayesian Transfer Bound: A bound on zero-shot transfer risk from training assets to a held-out asset, explicitly separating in-sample fit, model complexity, and distributional discrepancy (Theorem 3). This formalizes the intuition that foundation models require large pretraining panels to overcome complexity penalties.

4. Evaluation Framework

A robust statistical evaluation apparatus is employed:

Loss Functions: RMSE, MAE, and QLIKE (proven robust to noisy volatility proxies per Patton [31]).
Probabilistic Scoring: Continuous Ranked Probability Score (CRPS) for Gaussian predictive distributions.
Hypothesis Testing: Diebold–Mariano tests for pairwise accuracy and a stationary-bootstrap Model Confidence Set (MCS) for joint model comparison.
Data: A realistic synthetic panel of 20 assets generated from a Heston stochastic volatility model with jumps, allowing for the computation of realized quarticity and bipower variation directly from intraday paths.

Key Results

1. Performance Hierarchy

TSFM vs. GARCH/EWMA: The TSFM-surrogate statistically significantly outperforms GARCH(1,1) and EWMA across all loss functions (RMSE, QLIKE) and testing procedures (Diebold–Mariano, MCS).
TSFM vs. HAR Family: The TSFM-surrogate is significantly outperformed by the entire HAR family (HAR-RV, HARQ, HAR-CJ) in pairwise Diebold–Mariano tests. HARQ and HAR-CJ achieve the lowest error rates, confirming the value of jump and measurement-error robustness in the synthetic data-generating process.
Model Confidence Set (MCS): Crucially, while pairwise tests show the TSFM is worse than HAR variants, the joint Model Confidence Set (90% confidence) includes the TSFM-surrogate alongside the entire HAR family. This indicates that, when accounting for multiple comparisons, the TSFM is statistically indistinguishable from the best-performing econometric models.

2. Context Length and Architecture

Context Ablation: Zero-shot accuracy improves monotonically as the transformer's context window increases (from $L=16$ to $L=64$ ). The $L=64$ variant outperforms the $L=32$ baseline, suggesting the model has not yet saturated the benefits of longer lookback horizons, mirroring HAR's reliance on multi-month lags.
Calibration: The TSFM-surrogate's predictive distribution (via CRPS) is competitive with and slightly better calibrated than plain HAR-RV, highlighting the strength of its learned uncertainty quantification.

3. Computational Efficiency

While the TSFM-surrogate's single-sample forward pass is currently slower in wall-clock time than OLS-based HAR re-fitting at the sample sizes used ( $n \approx 1,250$ ), the paper argues that the practical advantage lies in amortization: a single frozen network serves all assets without per-asset re-estimation, eliminating the operational complexity of maintaining separate econometric pipelines.

Significance and Claims

The paper claims to provide a nuanced, mathematically grounded comparison rather than a simple "winner-takes-all" verdict. Its primary contributions are:

Refining the Paradigm Debate: The results suggest that long-memory autoregressive structures (HAR family) remain extremely difficult to beat on stationary, single-regime data. The TSFM's strongest claim is not that it "beats" HAR outright, but that it achieves statistical indistinguishability from the best models while offering the architectural advantage of zero per-asset re-estimation.
Theoretical Justification for Scale: Through Theorem 3 (PAC-Bayes bound), the paper formalizes that the TSFM's current disadvantage relative to HAR is partly due to the small pretraining panel ( $N=15$ ). The complexity penalty in the bound scales with $1/\sqrt{n}$ , implying that genuine uplift from foundation models likely requires pretraining on orders of magnitude more heterogeneous data to make the complexity term negligible.
Methodological Rigor: The paper establishes a reproducible protocol for evaluating foundation models in offline settings, proving that a custom-trained surrogate can validly test the paradigm (patch-attention, zero-shot transfer) without needing proprietary checkpoints.
Loss Function Sensitivity: The study demonstrates that model rankings and Model Confidence Set membership are not loss-invariant. The TSFM is excluded from the MCS under squared-error loss (due to sensitivity to volatility spikes) but included under QLIKE, reinforcing the need for robust loss functions like QLIKE in volatility forecasting.

In conclusion, the paper posits that while foundation models show promise and architectural expressiveness (proven via Proposition 5 to nest HAR structures), their practical superiority over classical econometrics in volatility forecasting is contingent on scale (large, heterogeneous pretraining panels) and deployment conditions (regime shifts, cross-asset heterogeneity) that were not fully present in this synthetic, single-regime study.