Denoised Return & Volatility Spillovers

Updated 3 September 2025

Denoised return and volatility spillovers are refined measures that filter out microstructure noise and extreme-event effects to accurately quantify risk transmission between markets.
Advanced econometric and machine learning techniques, including retarded feedback models, volatility decomposition, and network analysis, are employed to isolate persistent spillover channels.
These refined metrics inform improved risk management, portfolio allocation, and policy decisions by distinguishing genuine market signals from transient fluctuations.

Denoised return and volatility spillovers refer to the measurement and analysis of how standardized, noise-filtered financial returns—purged of transient, idiosyncratic, or microstructural fluctuations—propagate risk and uncertainty among assets or markets through their conditional variance dynamics. The literature integrates statistical, econometric, and machine learning tools to disentangle persistent interconnections in returns and volatilities from extraneous noise, with an emphasis on feedback, asymmetry, tail risk, and structural change mechanisms governing spillover effects.

1. Modeling Return–Volatility Correlation: Retarded Feedback and Large Volatility Events

A foundational insight is that the empirical return–volatility correlation—a principal driver of volatility spillovers—emerges from dynamic feedback interactions between returns and their time-lagged volatilities, rather than from static distributional asymmetries or volatility clustering alone (Shen et al., 2012). The retarded volatility model posits: $r(t') = [1 - \sum_{t=1}^\infty K(t) r(t' - t)] \sigma(t') \epsilon(t')$ with $K(t)$ representing the feedback kernel. Negative $K(t)$ yields a positive return–volatility correlation (anti-leverage effect, as in Chinese indices), while positive $K(t)$ produces the classical leverage effect (e.g., German DAX). Crucially, large returns (out-of-distribution, $|r| > 2\sigma$ ) dominate this effect, confirming that extreme events are the principal source of volatility spillovers across markets. Statistical “decoupling” of feedback via

$r_0(t') = [1 + \sum_{t=1}^\infty K(t) r(t'-t)] r(t')$

can eliminate the leverage effect without altering the marginal distribution or long-range volatility memory, isolating the dynamic spillover channel.

2. Volatility Decomposition, Denoising, and Microstructure Noise

Volatility decomposition models, especially in high-frequency contexts, clarify the origin of observed volatility fluctuations. The time-changed price model decomposes “clock-time” (calendar) volatility as

$\sigma_{\text{clock}}^2(t) = \sigma_t^2 \cdot \lambda_t$

where $\sigma_t^2$ is tick-time volatility and $\lambda_t$ is trading intensity (Dahlhaus et al., 2016). Tick-time volatility, being immune to changes in market activity, is empirically smoother and less exposed to microstructure noise. Pre-averaging and kernel smoothing estimators exploit this by separately estimating each component, yielding a denoised spot volatility estimator with superior convergence properties. This decomposition facilitates attribution of volatility spillovers to either event-driven price jumps or trading activity surges, allowing practitioners to “filter out” spurious or noisy spillovers and focus on persistent inter-market transmission.

3. Asymmetry and Directionality in Spillover Mechanisms

Empirical evidence demonstrates that the propagation of volatility across assets is highly asymmetric: negative (“bad”) shocks generate stronger and more persistent spillovers than positive (“good”) shocks (Barunik et al., 2014, Barunik et al., 2016, Hatemi-J, 19 Apr 2024). This is consistently observed in equity, petroleum, and FX markets:

Realized semivariances (RS $^-$ for downturns, RS $^+$ for upturns) parsed through VAR-GFEVD frameworks reveal that total and directional spillover indices are significantly higher for negative returns.
The asymmetry is quantified by measures such as the Spillover Asymmetry Measure (SAM): $\text{SAM} = 100 \times \frac{\mathcal{S}^+ - \mathcal{S}^-}{0.5(\mathcal{S}^+ + \mathcal{S}^-)}$ which is typically negative, validating the conjecture that risk transmission is biased towards downturns.

Extending traditional symmetric variance-decomposition methods, asymmetric connectedness models, e.g., Hatemi-J's AVD and time-varying quantile spillover frameworks, measure positive and negative shock spillovers separately, capturing the true heterogeneity in cross-market contagion (Hatemi-J, 19 Apr 2024, Fu et al., 30 Jul 2025). Application to equities, commodities, and cryptocurrencies consistently reveals greater spillover intensity during downside tail events, motivating adaptive risk management and conditional forecasting.

4. State-Dependence, Time Variation, and Network Structures

Volatility spillovers are not static: their magnitude and configuration change in response to structural events (financial crises, major policy interventions) and regime shifts in market states (Karanasos et al., 2014, Fu et al., 30 Jul 2025). During crisis periods, bivariate and multivariate GARCH or HAR-type models with abrupt break mechanisms detect heightened volatility persistence and spillover.

For example, dynamic conditional correlation models reveal jumps in both the level and persistence of spillovers during the 2008 global financial crisis.
The empirical role reversal of developed markets—transmitting risk under normal conditions but becoming net receivers during systemic stress episodes—is a stylized fact emerging from rolling-window, denoised VAR-spillover frameworks (Karasan et al., 1 Sep 2025).

Advanced models incorporate network structures and clustering via weight matrices computed from both raw and model-implied distances (e.g., DCC, GO-GARCH, Piccolo). In network-based log-ARCH, the conditional volatility at each node (country or asset) is influenced by both its own lagged volatility and the contemporaneous volatility of its network neighbors, objectively capturing instantaneous cross-asset spillover channels (Djebari et al., 20 Jul 2025). Network centrality and preferential attachment effects, empirically supported by spatial probit models, further reveal that highly connected markets act as spillover “hubs” (Lyocsa et al., 2015).

5. Denoising Techniques: From Distributional Filtering to Machine Learning

Denoising financial returns to extract persistent spillover patterns involves both parametric and data-driven approaches:

Distributional correction addresses the excess volatility puzzle by fitting heavy-tailed return models (log-NIG, NCIG), substantially reducing the spurious variability in forecast volatility and clarifying genuine spillover magnitudes (Shirvani et al., 2020).
Model-based denoising (e.g., ARFIMA-GARCH and structured network shrinkage) removes predictable and high-frequency “noise,” permitting Granger causality or variance decomposition analysis on standardized residuals (Lyocsa et al., 2015).
Machine learning–based methods, such as neural-network denoisers (Karasan et al., 1 Sep 2025), use learned mappings to clean sample covariance matrices before spillover estimation. The architecture (deep feed-forward network with GELU activation, normalization, and eigenvalue thresholding) ensures positive-definite, symmetric denoised matrices. Empirically, incorporating denoised covariances yields spillover indices more robust to microstructure errors and better aligned with financial events.

In generative frameworks, conditional diffusion models incrementally remove noise from time series via learned reverse SDEs, resulting in series with improved trend fidelity and reduced spurious volatility. This directly enhances downstream return prediction and trading performance by sharpening the distinction between meaningful trends and spurious reversals (Wang et al., 2 Sep 2024).

6. Practical and Policy Implications

Denoised return and volatility spillover measures have direct applications in:

Risk management: Denoised volatility series allow for accurate estimates of Value-at-Risk, capital requirements, and scenario analysis. The enhanced clarity in risk transmission paths enables early warning systems for crisis periods (Chiua et al., 2022).
Portfolio construction: More precise spillover indices inform allocation decisions and hedging strategies, particularly in periods of increased tail risk or asymmetric contagion.
Policy analysis: Systemic risk monitoring benefits from denoised, time-varying spillover measures that distinguish between transient spikes and structural shifts in interconnectedness, supporting macroprudential regulation, especially for sectors reliant on external financing or exposed to global commodity cycles.
Algorithmic trading: Strategies operating on denoised data yield improved profitability, lower transaction costs, and better adaptation to regime shifts, as classifiers can distinguish noisy from actionable market states (Wang et al., 2 Sep 2024).

7. Limitations and Theoretical Insights

Despite methodological advances, inherent information-theoretic bounds—quantified via Shannon mutual information in stochastic volatility models—suggest that even at very high frequencies, observed returns may contain limited information about the latent volatility process or cross-asset spillovers (Pfante et al., 2016). This fundamental limitation underscores the need for advanced denoising, but also places a ceiling on achievable predictability, motivating ongoing research into richer observational and joint-model frameworks.

In summary, the literature establishes that denoising techniques—spanning distributional filtering, volatility decomposition, machine learning, and structural network modeling—are indispensable for isolating true return and volatility spillovers in financial markets. This leads to more accurate risk assessment, enhanced econometric identification of systemic transmission channels, and improved decision-making for both practitioners and policymakers in environments characterized by episodic shocks, heavy tails, and evolving market interdependencies.