Regime-Adaptive Hawkes Processes for Predicting Crypto Market Cascades

Regime-Adaptive Hawkes Processes for Predicting Crypto Market Cascades

Detecting Large-Move Clusters Across BTC, ETH and SOL

This blog post was written by Talin Gaur, a Quantitative Researcher at the Indian Institute of Technology (IIT) Jodhpur specializing in financial time-series modeling, signal extraction, and matrix de-noising. Talin focuses on statistical alpha generation, applying Hidden Markov Models, Random Matrix Theory, and high-dimensional noise filtering to systematic trading systems. He has hands-on experience in quantitative research through roles at IndiQuant and WorldQuant, where he works as a Research Consultant. His competitive record includes a Global Rank of 209 (Top 0.14%) in the International Quant Championship 2026, an All India Rank of 39 in Stage 1 (Top 0.07%), and a National Rank of 351 in QuantStorm. He also placed in the top 0.7% nationally in JEE Mathematics. Outside of his research, Talin is focused on bridging probability theory, stochastic calculus, and statistical machine learning to solve complex market problems. Connect with Talin on LinkedIn or access the full research behind this blog post on SSRN.

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Cryptocurrency markets frequently experience periods in which unusually large price movements occur close together in time. Such clustering creates a natural setting for self-exciting point-process models.

This study investigates whether a multivariate Hawkes process can identify clusters of large movements across Bitcoin (BTC), Ethereum (ETH), and Solana (SOL), and whether adapting the Hawkes dynamics to the prevailing market-activity regime improves out-of-sample cascade prediction.

Hourly market data are converted into asset-specific large-move event streams. A standard multivariate Hawkes process is first estimated to capture temporal and cross-asset excitation. A regime-adaptive extension then conditions the event dynamics on recent market activity, measured using lagged 24-hour average absolute returns.

The main prediction target is a cross-asset cascade, defined as at least two large-move events occurring across BTC, ETH, and SOL within the next six hours. The evaluation uses a chronological train/test separation.

For the six-hour target, the standard Hawkes model achieves a ROC-AUC of approximately 0.613 and a PR-AUC of 0.147. The regime-adaptive model achieves a ROC-AUC of approximately 0.646 and a PR-AUC of 0.152. The adaptive model also remains above the standard specification across the tested three-hour, six-hour, and twelve-hour horizons.

A secondary timing-safe risk-management backtest illustrates how the predicted cascade intensity can be converted into a dynamic exposure signal. The results are presented as a research and risk-analysis framework rather than as a claim of guaranteed trading performance.

Introduction

Cryptocurrency markets often experience periods in which large price movements arrive close together in time. A sharp movement in one asset may be followed by unusually large movements in another, producing short-lived episodes of elevated market activity.

From a modelling perspective, this behaviour is different from a setting in which extreme events occur independently. The occurrence of one large event may temporarily increase the likelihood of subsequent events. In addition, the interaction between assets may matter: a large movement in Bitcoin may coincide with or precede large movements in Ethereum or Solana.

This creates a natural application for Hawkes processes. A Hawkes process is a self-exciting point process in which the occurrence of an event temporarily increases the conditional intensity of future events. In a multivariate setting, the framework can also represent cross-excitation between different event types.

The central question of this study is: can a regime-adaptive Hawkes process improve the out-of-sample prediction of short-horizon cross-asset cryptocurrency cascades?

The study compares a standard multivariate Hawkes model with a regime-adaptive extension. The latter allows the estimated event dynamics to respond to the recent level of market activity.

The analysis is focused on event clustering rather than directional price forecasting. A high predicted event intensity indicates elevated risk of future large-move activity; it does not specify whether the underlying price movement will be positive or negative.

Data and Event Construction

The analysis uses hourly price data for three major cryptocurrency assets — Bitcoin (BTC), Ethereum (ETH), and Solana (SOL), sourced from Yahoo Finance — covering approximately September 2024 to September 2026.

For each asset, hourly log returns are calculated. The absolute value of the hourly log return is then used as a measure of the magnitude of the movement:

$$r_{i,t} = \log\left(\frac{P_{i,t}}{P_{i,t-1}}\right)$$

where $P_{i,t}$ denotes the price of asset $i$ at time $t$.

Large-move events are defined using asset-specific absolute-return thresholds. This allows the event definition to account for differences in the typical volatility of BTC, ETH, and SOL. The resulting data can therefore be viewed as three event streams: $E_{BTC}$, $E_{ETH}$, $E_{SOL}$.

The distributions of absolute hourly returns are heavily concentrated near zero while exhibiting long right tails.

Figure 1: BTC — Absolute Hourly Return Distribution.

The corresponding distributions for ETH and SOL display similar right-skewed behaviour.

Evidence of Event Clustering

Before fitting a Hawkes process, it is useful to examine whether the event data exhibit temporal clustering.

The distribution of inter-event times is strongly concentrated at short intervals, with progressively fewer observations at longer time separations.

Figure 2: Distribution of inter-event times across the large-move event process.

The event autocorrelation also remains positive beyond the contemporaneous observation. This provides empirical motivation for using a self-exciting point process rather than treating each large-move event as independent.

The purpose of this diagnostic is not to establish a causal relationship, but rather to identify temporal structure that a Hawkes process can potentially capture.

The Multivariate Hawkes Process

For asset $i$, the conditional intensity of the Hawkes process is written as:

$$\lambda_i(t) = \mu_i + \sum_j \alpha_{ij} \sum_k \exp\left[-\beta\left(t - t_k^{(j)}\right)\right]$$

Here, $\mu_i$ is the baseline intensity for asset $i$, $\alpha_{ij}$ controls the excitation from event type $j$ to event type $i$, $\beta$ controls the decay rate of excitation, and $t_k^{(j)}$ denotes previous event times for asset $j$.

This specification allows the model to capture two forms of dependence. Self-excitation: events in one asset temporarily increase the likelihood of future events in that same asset. Cross-excitation: events in one asset can temporarily increase the likelihood of events in another asset.

The resulting branching matrix provides a compact representation of these interactions.

Figure 3: Estimated branching matrix for the standard Hawkes process.

The diagonal elements represent within-asset excitation, while the off-diagonal elements represent cross-asset contributions.

Defining a Market Cascade

The objective is not to predict the next individual large-move event. Instead, the model is used to predict whether a short-horizon cross-asset cascade will occur.

The primary target is defined as:

$$Y_t = \begin{cases} 1, & \text{if at least two large-move events occur in the next 6 hours} \\ 0, & \text{otherwise} \end{cases}$$

The event count is considered across BTC, ETH, and SOL. Only events occurring after the prediction timestamp are used to define the target — this makes the prediction problem forward-looking. The aggregate Hawkes intensity is then used as a predictive signal for the probability of a future cascade.

Out-of-Sample Evaluation

The evaluation uses a chronological train/test separation. The earlier observations are used for model estimation and the later observations are reserved for out-of-sample evaluation. No random shuffling is used.

Concretely, the data is split 70/30 chronologically, with the training period ending on 7 February 2026 and the remaining period held out strictly for out-of-sample evaluation. The regime thresholds and all model parameters are estimated using only the training period; the out-of-sample intensities use only information available up to each prediction timestamp.

This design is important for financial time-series research because a random split can allow information from later market conditions to enter the training sample. The intended experimental structure is therefore:

Historical data → Training period → Unseen test period.

The model is evaluated only on the observations that were not used for parameter estimation.

Standard Hawkes Cascade Prediction

The standard Hawkes process generates an aggregate event intensity that acts as a measure of current cascade risk. A useful diagnostic is to divide the out-of-sample observations into intensity deciles and compare the observed future cascade frequency.

Figure 4: Observed out-of-sample cascade rate across standard Hawkes intensity deciles.

The highest-intensity observations exhibit substantially higher observed cascade rates than many lower-intensity observations. This provides a useful sanity check that the estimated intensity contains information about subsequent event clustering.

The standard Hawkes model achieves an out-of-sample ROC-AUC of approximately 0.613. The corresponding PR-AUC is approximately 0.147, compared with a random-classifier baseline of approximately 0.071.

Introducing Market-Activity Regimes

A standard Hawkes process assumes that one set of event dynamics is sufficient to describe the entire sample. However, cryptocurrency markets can move between relatively quiet periods and periods of substantially elevated activity.

To account for this, a market-activity regime variable is introduced. The regime is based on the lagged 24-hour average absolute return:

$$A_t = \frac{1}{24} \sum_{h=1}^{24} |r_{t-h}|$$

The market is classified into three activity regimes: low activity, normal activity, and high activity. The regime thresholds are determined using the training period. The use of lagged activity is important because the regime variable must only contain information available at the time of prediction.

Figure 5: Lagged 24-hour market activity and regime thresholds.

Regime-Adaptive Hawkes Process

The regime-adaptive extension retains the Hawkes-process structure while allowing its parameters to vary with the prevailing market-activity regime. Conceptually, the intensity can be written as:

$$\lambda_i(t \mid R_t) = \mu_{i,R_t} + \sum_j \alpha_{ij,R_t} \sum_k \exp\left[-\beta_{R_t}\left(t - t_k^{(j)}\right)\right]$$

where $R_t$ denotes the current market-activity regime.

The motivation is straightforward. A Hawkes process estimated under relatively calm market conditions may not describe event propagation during a period of extreme activity equally well. Allowing the model to adapt to recent market activity provides a mechanism for capturing changes in event dynamics.

The resulting out-of-sample adaptive intensity is shown below.

Figure 6: Regime-adaptive Hawkes out-of-sample intensity and future cascade observations.

Out-of-Sample Results

The primary six-hour cascade experiment produces the following results.

Model	ROC-AUC	PR-AUC
Standard Hawkes	0.613	0.147
Regime-Adaptive Hawkes	0.646	0.152
Random PR baseline	–	0.071

The regime-adaptive model therefore produces a higher ROC-AUC and PR-AUC than the standard Hawkes benchmark.

Figure 7: Out-of-sample ROC comparison between standard and regime-adaptive Hawkes models.

The precision-recall comparison is particularly useful because cascade events are less frequent than non-cascade observations.

Figure 8: Out-of-sample precision-recall comparison.

The adaptive model remains above the standard benchmark over substantial parts of the precision-recall curve. The improvement is meaningful as a modelling result, but it should not be interpreted as a deterministic prediction of future market cascades.

Robustness Across Prediction Horizons

To test whether the result depends specifically on the six-hour target, the experiment is repeated using three different cascade horizons: 3 hours, 6 hours, and 12 hours.

The regime-adaptive model remains above the standard Hawkes model across all three tested horizons.

Figure 9: Out-of-sample ROC-AUC across three, six, and twelve-hour cascade horizons.

The persistence of the improvement across different prediction horizons reduces the extent to which the result depends on one arbitrarily chosen target window.

From Prediction to Risk Management

Prediction performance and trading performance are different questions. A model can identify periods of elevated event risk without necessarily generating a profitable directional trading strategy. For this reason, the trading component of this study is treated as a secondary risk-management application.

The basic idea is to use predicted cascade intensity as a risk signal. When predicted risk becomes sufficiently high, portfolio exposure can be reduced. When predicted risk declines, normal exposure can be restored. This converts the Hawkes intensity into a potential dynamic exposure signal rather than a direct price forecast.

Timing-Safe Risk-Management Backtest

The risk-management experiment compares Market Buy-and-Hold, Standard Hawkes risk management, and Regime-Adaptive Hawkes risk management.

The final backtest is timing-safe: the signal is applied only to the following return period. This is important because using information from the current return period to determine exposure to that same return would introduce look-ahead bias.

Figure 10: Timing-safe out-of-sample risk-management backtest.

The backtest is intended to demonstrate how an event-risk prediction model could be incorporated into portfolio risk management. It should not be interpreted as evidence of guaranteed live-trading profitability.

Backtest Diagnostics

The broader backtest diagnostics report total return, annualized Sharpe ratio, maximum drawdown, annualized volatility, and the number of risk-off hours.

Strategy	Return	Sharpe	Max DD	Volatility	Risk-Off Hours
Market Buy/Hold	18.14%	0.926	-34.18%	46.95%	0
Standard Hawkes	-11.73%	-0.509	-25.85%	35.42%	399
Regime-Adaptive Hawkes	15.09%	0.893	-24.29%	39.28%	361

These values should be interpreted as diagnostic results from the backtesting experiment. In particular, the timing-safe equity curve in Figure 10 is the appropriate representation of the final timing-safe experiment.

The study does not incorporate a formal transaction-cost or turnover model. Therefore, the reported backtest statistics should not be interpreted as net-of-cost live-trading performance.

What Does the Model Actually Predict?

The model is not designed to predict the next BTC, ETH, or SOL price. It also does not directly predict whether the next large movement will be positive or negative. Instead, it estimates the intensity of future large-move activity. A high predicted intensity means that the model assigns greater likelihood to a future cluster of large events.

This distinction makes the framework naturally suited to applications such as portfolio risk monitoring, dynamic exposure reduction, volatility monitoring, stress detection, event-risk forecasting, and short-horizon market activity monitoring.

The framework therefore focuses on when the market may become more susceptible to clustered extreme movements rather than attempting to forecast the exact direction of prices.

Why Regime Adaptation Matters

The standard Hawkes process already captures temporal clustering and cross-asset excitation. The regime-adaptive extension adds another layer by allowing these event dynamics to depend on recent market activity. This is motivated by the possibility that the propagation of extreme events is not stationary across all market environments — a relatively quiet market may exhibit different event dynamics from a period of elevated activity.

The reported results suggest that conditioning the Hawkes framework on recent market activity provides additional information for out-of-sample cascade prediction. The main six-hour experiment shows higher ROC-AUC and PR-AUC for the adaptive model, while the robustness analysis shows that the ROC-AUC advantage persists across three-, six-, and twelve-hour horizons.

Limitations

Limited asset universe. The analysis focuses on BTC, ETH, and SOL. A broader cross-sectional universe could provide a more comprehensive representation of cross-asset cryptocurrency contagion.

Event definition. Large-move events depend on asset-specific return thresholds. Different threshold choices could alter event frequencies and therefore influence the estimated Hawkes dynamics.

Statistical dependence is not causality. Hawkes excitation parameters describe statistical dependence within the model. They should not be interpreted as proof that movement in one cryptocurrency mechanically causes movement in another.

Finite out-of-sample period. The model is evaluated over a finite historical test period. Out-of-sample performance over one historical period does not guarantee future performance.

Transaction costs and turnover. The current risk-management experiment does not incorporate a formal transaction-cost or turnover model. A practical implementation would need to account for trading costs, execution effects, liquidity, and the frequency of exposure changes.

Risk-management interpretation. The trading experiment is intended as an illustration of how the prediction signal could be used for risk management. It is not presented as evidence of guaranteed or persistent live-trading alpha.

Conclusion

This study develops a regime-adaptive Hawkes-process framework for modelling clusters of large cryptocurrency movements across BTC, ETH, and SOL. The standard Hawkes model captures both self-excitation and cross-asset excitation between large-move events. The regime-adaptive extension additionally incorporates recent market-activity conditions, allowing the event dynamics to respond to different levels of market activity.

For the six-hour cascade target, the standard Hawkes model achieves a ROC-AUC of approximately 0.613 and a PR-AUC of 0.147. The regime-adaptive model achieves a ROC-AUC of approximately 0.646 and a PR-AUC of 0.152. The improvement also persists across the three-hour, six-hour, and twelve-hour prediction horizons.

These results suggest that recent market activity contains information that can improve the modelling of short-horizon cross-asset event clustering beyond a fixed Hawkes specification. The secondary risk-management experiment demonstrates how the resulting event intensity can be translated into a dynamic exposure signal. However, transaction costs, turnover, liquidity, and longer evaluation periods would need to be incorporated before making claims about practical live-trading performance.

The broader objective of the framework is therefore not simply to predict whether cryptocurrency prices will rise or fall. Instead, it asks a more specific question:

When is the market becoming structurally more likely to experience another cluster of extreme movements?

This event-intensity perspective provides a useful framework for monitoring and managing short-horizon market risk in interconnected cryptocurrency markets.

Research Materials

The analysis was implemented in Python and includes hourly cryptocurrency return construction, large-move event construction, event-time diagnostics, multivariate Hawkes-process estimation, branching-matrix analysis, out-of-sample cascade prediction, ROC and precision-recall evaluation, market-activity regime classification, regime-adaptive Hawkes estimation, robustness analysis across prediction horizons, and timing-safe risk-management backtesting.

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Talin Gaur is a Quantitative Researcher at the Indian Institute of Technology (IIT) Jodhpur. Connect with him on LinkedIn.