Predictive Analysis of Whale Impact on Bitcoin Volatility

Bruno de Almeida Lemes; Lilian da Silveira

DOI: 10.22167/2675-6528-202602737

Article derived from a Course Conclusion Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The change in the cryptoasset market, driven by the launch of Bitcoin ETFs in 2024, integrated institutional investors, requiring the adaptation of volatility analysis models traditionally dedicated to the stock market. The study aimed to validate whether behavioral metrics of large investors, known as whales (flow and short-term movements), or balance metrics (volume under management or possession), had greater predictive power over Bitcoin’s future volatility. To this end, the Heterogeneous Autoregressive model with eXogenous variables (HAR-X) was applied to evaluate and compare the impact of these metric classes on the asset’s future 7-day volatility. 3,277 daily quotation records of the cryptocurrency’s price and “on-chain” classifications already generated by Glassnode, covering the period from 2017 to 2025, were used. The results revealed that, contrary to the initial hypothesis, the model focused on balance metrics showed superior predictive capacity in the test scenario, with an R² of 0.826. It was concluded that the concentration of the asset, especially in the possession of long-term holders, acts as the main buffer for Bitcoin’s volatility.

Keywords: Whales; Bitcoin; HAR-X; Regression.

1. Introduction

The creation of Bitcoin in October 2008 marked the emergence of a new asset class in the global market. Unlike traditional markets, Bitcoin operated without direct regulation by agents such as Central Banks and without collateral for its value (Hernández, 2022).

In the following decade, what began as a niche project for technology and cryptography enthusiasts expanded exponentially. Several new “tokens”, units of digital value issued on blockchain platforms (Harvey et al., 2021), emerged, adding functionalities such as smart contracts and tokenization of real assets. This ecosystem demonstrated constant growth, with the total market value of cryptoassets reaching four trillion dollars in September 2025, an increase of more than 2,500% since 2013 (Coinmarketcap, 2025).

Until 2024, most of this capitalization was concentrated in individuals and cryptocurrency brokers. However, the U.S. Securities and Exchange Commission (SEC) approval for the first issuance of Bitcoin-linked ETFs (Exchange-Traded Funds) signaled the legitimization of the digital currency as an institutional-grade asset. This allowed individuals and legal entities to access this asset class through traditional companies, increasing the market’s capillarity and capitalization. In October 2025, these ETFs reached a volume of over 190 billion dollars under management, representing a 678% growth in just over 20 months (Coinmarketcap, 2025).

Complementing this institutionalization, the emergence of “treasury companies” was observed, companies whose business model is based on the purchase of cryptoassets with their cash, such as Microstrategy (Bloomberg, 2025). This new scenario has profoundly altered the profile of participants in the digital asset market, from large management funds to companies dedicated to the purchase of cryptocurrencies. The change in the profile of traders demands a new approach to analyzing price fluctuations, especially regarding the performance of passive long-term investors and high-frequency traders.

The analysis of the impact of large “players”, known as “whales”, on price formation is an already established problem in the traditional market. Price formation is the process by which information, public or private, is assimilated and incorporated into an asset’s price through trading dynamics (O’Hara, 1995). Previous studies have shown that institutional investors, due to their “herding” behavior and access to superior information, generate significant and predictive impacts on stock returns (Gompers and Metrick, 2001). It is argued that a similar dynamic occurs in the crypto-asset market, and the availability of “on-chain” data allows for the evaluation of these movements in real-time. Recent research in crypto has already validated this premise, showing that whale flows to exchanges have a statistically significant and negative impact on Bitcoin prices (Cong et al., 2022).

Given the increasing institutionalization of Bitcoin and the recognized influence of large investors, it becomes essential to deepen the understanding of how the actions of these agents impact the asset’s volatility. Thus, the present work seeks to validate whether behavioral metrics of whales, compared to traditional metrics based on balance ranges, have greater predictive power for the future volatility of Bitcoin, especially in the post-approval context of spot ETFs in January 2024.

2. Material and Methods

This work was characterized as an applied research, quantitative in nature, with explanatory objectives. Regarding technical procedures, it was classified as ex-post-facto documentary research, using secondary data from financial market platforms. The development of the study followed the CRISP-DM (Cross-Industry Standard Process for Data Mining) methodology, as proposed by Shearer et al. (2000), a structured approach widely used in data analysis and science.

Data collection was performed from two main sources. Bitcoin price quotes were extracted from Yahoo Finance, through its open API and the yfinance library in Python. Behavioral and balance data, which formed the basis for the “whales” metrics, were obtained from the Glassnode website, through extractions in .csv files for each specific variable.

Bitcoin price data, obtained from Yahoo Finance, presented daily granularity and included information such as maximum, minimum, and closing prices, in addition to the volume traded on the day. This information was fundamental for the calculation of volatility, which served as the response variable of the predictive model.

Several “on-chain” metrics were collected from Glassnode. Balance metrics included the total amount of Bitcoin in addresses that have not moved their cryptocurrencies for 155 days or more, termed Long-Term Accumulators. Bitcoin concentration in addresses by volume was also used, segmented into three ranges: 1,000 to 10,000 BTC, 10,000 to 100,000 BTC, and above 100,000 BTC, expressed as a percentage of the total available volume.

Glassnode’s behavioral metrics encompassed the Long-Term Holder Accumulator Balance Change, which indicated the daily variation in the volume of Bitcoins held by these holders. The Exchange Inflow Volume quantified the total Bitcoin transferred from private wallets to exchanges, and the Net Exchange Position Change represented the difference between the inflow and outflow of Bitcoin from exchanges.

For each of the original Glassnode metrics, with the exception of the Change in Long-Term Holder Balance, seven-day changes were calculated. These derived features were obtained by the difference between the current value and the value from seven days prior, aiming to capture short and medium-term trends in the behavior and distribution of “whales”.

The analysis period comprised daily observations from January 1, 2017, to December 21, 2025, totaling 3,277 records. This temporal interval was selected to encompass multiple Bitcoin market cycles, including periods of high and low volatility, and the structural change resulting from the approval of Bitcoin ETFs in January 2024.

The data preparation stage involved unifying information from Yahoo Finance and Glassnode. The integration was performed using the pandasql library in Python, which allowed for the cross-referencing of daily databases through the date field, resulting in a unique dataset with all collected variables.

The dependent variable, future volatility, was calculated as the standard deviation of daily returns observed in subsequent seven-day rolling windows (Hull, 2018). Daily returns were calculated as simple returns, where P_t represented the closing price of Bitcoin on date t. Additionally, backward-looking moving averages of volatility itself were calculated for past one-, seven-, and thirty-day windows, serving as market memory components.

For preprocessing, the winsorization technique was applied at the fifth and ninety-fifth percentiles to all independent variables in the model. This approach was used to mitigate the influence of extreme values without completely removing data from the sample, contributing to the stability of the estimates. It was decided not to shuffle the data, maintaining the continuous temporal sequence of Bitcoin quotes.

The division of data into training and testing sets was performed with a temporal split on January 1, 2025. The training set covered the period from January 1, 2017, to December 31, 2024, totaling 2,922 observations (89% of the total). The test set comprised January 1, 2025, to December 21, 2025, with 355 observations (11% of the total), allowing for the evaluation of the model’s generalization capability on unseen data.

For the modeling, the HAR-X econometric model (Heterogeneous Autoregressive model with eXogenous variables) was used, an extension of the HAR model proposed by Corsi (2009). The HAR-X model incorporates exogenous variables into the heterogeneous autoregressive structure of the classic HAR model, which considers the influence of past volatility at different time horizons (daily, weekly, and monthly).

In the context of the crypto-asset market, the HAR model’s time windows were adapted from five and twenty-two business days to seven and thirty calendar days, respectively, reflecting the market’s uninterrupted operation. Four distinct HAR-X models were estimated for comparison: Basic HAR (autoregressive components only), Behavioral HAR-X (adding six behavioral variables), Balance HAR-X (adding eight balance variables), and Full HAR-X (containing all seventeen predictor variables simultaneously).

The choice of the HAR-X model was justified by its validation in the finance literature for cryptocurrency volatility forecasting (Aalborg et al., 2019), its robust interpretability through coefficients and p-values, and its suitability for handling the limited volume of available data (2,892 observations), minimizing the risk of overfitting compared to more complex machine learning algorithms.

The training of the four models was performed using the ordinary least squares method (OLS), with the application of Newey-West Heteroskedasticity and Autocorrelation Consistent (HAC) error correction. The “maxLags” parameter of the HAC correction was adjusted from five to seven, aligning with the seven-day dynamics of the cryptoasset market.

The CRISP-DM methodology also included the evaluation and deployment steps. In evaluation, the performance of the developed models was measured to determine the adequacy of the results to the established objectives. The deployment step focused on documenting and organizing the results to ensure the reproducibility and dissemination of the generated knowledge, given the academic purpose of the study.

Glassnode’s “on-chain” metrics were classified for better understanding of their representativeness. Variables such as “Exchange Inflows” and “Net Exchange Balance” were classified as behavioral, representing aggregate market flows. The “Long-Term Holder Net Position Change” was also considered behavioral, indicating the pace of accumulation or distribution.

On the other hand, the “Total Long-Term Holders Balance” and the “Whale Balance” variables segmented by volume ranges (1k-10k, 10k-100k, >100k BTC) were classified as balance metrics. The latter represented the only classification strictly segmented by wallet size, reflecting the volume of Bitcoin held by different categories of large investors.

3. Results and Discussion

This section details the results obtained from applying the four estimated econometric models: Basic HAR, Behavioral HAR-X, Balance HAR-X, and Complete HAR-X. The analysis aims to understand the predictive capacity of different classes of “on-chain” metrics on Bitcoin’s future volatility, in line with the study’s objective. The findings are presented in a structured manner, addressing data characterization, model performance, coefficient analysis, and statistical validations, culminating in an in-depth discussion of the results’ implications.

The dataset used for the analysis comprised 3,277 daily observations, covering the period from January 1, 2017, to December 21, 2025, totaling approximately nine years of data. This temporal interval was strategically selected to capture multiple Bitcoin market cycles, including phases of high volatility, such as the “bull markets” of 2017 and 2021, and periods of low volatility, such as the “bear markets” of 2018 and 2022. The inclusion of the period after the approval of Bitcoin ETFs in January 2024 was crucial for analyzing the structural shift in the market.

The 7-day future volatility, defined as the model’s response variable, presented an average of 3.1% with a standard deviation of 1.9%. A minimum value of 0.2% and a maximum of 15.9% were observed for this metric, which reinforces Bitcoin’s cyclical nature, characterized by alternation between periods of strong accumulation and low volatility, and high volatility events. This variability is a central aspect for understanding the risk associated with the asset, as discussed by Fidelity (2026).

Behavioral metrics, which capture short-term flows and movements, revealed important patterns. The average daily inflow of Bitcoin into exchanges was 46,302 BTC, with a standard deviation of 24,272 BTC. This high variability indicates that, on certain days, flows to centralized exchanges are significantly higher than the average. Such a pattern suggests that large, one-off Bitcoin movements to exchanges may precede periods of higher volatility, aligning with market intuition that transfers to exchanges often signal selling intent (Kraken Intelligence, 2026).

In contrast, metrics related to balance and holdings, which reflect asset concentration, indicated a significant distribution in addresses with large volumes. The total volume of Bitcoin held by long-term holders (LTH Supply) reached an average of 12.52 million BTC, representing approximately 63% of the total circulating supply. This high proportion suggests that the majority of Bitcoin is in the hands of long-term accumulators, known as “strong hands”, who historically demonstrate lower sensitivity to short-term fluctuations, contributing to market stability.

The concentration of Bitcoin in wallets with balances between 10,000 and 100,000 BTC, with an average of 13.13% of the supply, proved particularly relevant for the study. This balance range is crucial because it represents large-sized wallets that are not exchanges, but also not retail investors. Such wallets, often associated with treasury companies, like Microstrategy, and institutional funds, were the main focus of the analysis, given the growing institutionalization of the crypto-asset market.

In evaluating the performance of the models, all four presented consistent performance between the training and testing sets, with R² values above 0.81 in both scenarios. This consistency is an indicator of good generalization capability and absence of “overfitting”, a common problem in machine learning models with limited data (Hastie, 2009). Model robustness is fundamental for the validity of predictions.

The HAR-X Saldo model stood out as the best performing on the test set, achieving an R² of 0.826. This result means that the model is capable of explaining 82.6% of the variance in future Bitcoin volatility. This performance was marginally superior to that of the HAR-X Behavioral model, which obtained an R² of 0.817, and to the Basic HAR, with an R² of 0.819. This finding contradicts the study’s initial hypothesis, which predicted greater predictive power for behavioral metrics.

The joint inclusion of balance and behavioral variables in the Complete HAR-X model, which contained all 17 predictors, did not result in a significant additional improvement in predictive performance, presenting an R² of 0.825. This result, slightly lower than that of the HAR-X Balance model, was counterintuitive and suggests that the simultaneous inclusion of all variables may not bring a relevant increase, possibly due to complex interactions or redundancies between the metrics.

In terms of prediction error, the MAE (Mean Absolute Error) of the HAR-X Saldo model was 0.002631. This value indicates an average error of approximately 0.26 percentage points in the prediction of future volatility, which is considered a satisfactory result, especially when compared to the average volatility of the period, which was 3.06%. In practical terms, this implies that the model errs, on average, less than 10% of the actual value of volatility, offering a precise measure for risk management.

To complement the analysis of R² and MAE, the incremental F test was performed, which confirmed that both behavioral and balance metrics significantly improve the fit of the Basic HAR model (p < 0.001 in both cases). This validates the premise that the movements and distributions of large investors contain relevant predictive information for future Bitcoin volatility, even after controlling for the persistence of volatility itself captured by the autoregressive components.

The comparison between the Behavioral HAR-X model and the Complete HAR-X also proved to be statistically significant (F=3.30, p<0.001). This result indicates that the addition of balance metrics to a model that already incorporates behavioral metrics brings incremental information. Although the Balance HAR-X model, by itself, already shows a performance comparable to the Complete model, the incremental significance reinforces the complementarity between the two types of metrics in explaining volatility.

The detailed analysis of the coefficients of the variables used in the Full HAR-X model revealed that only four out of fourteen variables showed statistical significance (p-value < 0.05). Three of these variables are behavioral in nature and one is a balance, providing specific insights into the impact of each on future Bitcoin volatility. This selectivity in predictor significance is crucial for a more precise understanding of market mechanisms.

The “Entry into Brokerages” variable showed a negative coefficient (-1.66×10-8) and a p-value of 0.04. This result suggests that increases in the volume of Bitcoins sent to brokerages are associated with drops of approximately 0.016 percentage points in the 7-day future volatility. This indicates that the impact of these movements is short-term, with a large part of the effect already absorbed within the one-week window, leading to more controlled volatility after this initial period.

The “Brokerage Entry Variation (7d)”, with a negative coefficient (-3.87×10-8) and a p-value of 0.00, reinforces the thesis of the relevance of flow for brokerages and the immediate nature of its impact. The statistical significance of this variable corroborates the interpretation that, after seven days, the initial “shock” in volatility has already dissipated, and the market tends to return to a state of greater control. Both brokerage entry metrics, therefore, point to a rapid adjustment dynamic.

The “Net Balance in Brokerages” exhibited a positive coefficient (6.59×10-9) and a p-value of 0.04. This finding suggests that a positive change in the net position of Bitcoins held in brokerages is associated with an increase in future volatility. This may indicate that the growth in the total balance in brokerages precedes liquidations in a longer term than daily, differentiating itself from variables that only measure resource inflow, and suggesting a future selling intention.

The variable “Total Balance of Long-Term Holders (LTD)” presented a negative coefficient (-6.72×10-10) and a p-value of 0.00. This result is particularly relevant, as it demonstrates that “long term holders” contribute to a perception of security and stability in the market. The increase in Bitcoin holdings by these long-term holders is associated with a reduction in the asset’s future price volatility, acting as a buffer against short-term fluctuations.

Despite the relevant insights provided by the individual analysis of the variables, it is fundamental to consider the joint behavior and possible cross-influences, especially in a model with several predictor variables. The Variance Inflation Factor (VIF) test was applied to assess the presence of multicollinearity, which measures how much the variance of a regression coefficient is inflated due to correlation with other predictor variables (Wooldridge, 2016).

The VIF test results indicated high multicollinearity for the variables “Whale Balance (10k-100k)”, with a VIF of 18.82, and “Whale Balance (1k-10k)”, with a VIF of 8.81. Although the latter is below the limit of 10 proposed by Hair (2010), its proximity suggests a high level of collinearity. These high values indicate that the accumulated amount by these “whales” is, in fact, a result of other market movements, such as the flow to exchanges or the variation in the flow of long-term holders, suggesting that these whales may be, in part, the long-term holders of Bitcoin themselves.

This finding of high multicollinearity is a strong indicator of why the Complete HAR-X model did not outperform the Balance HAR-X model in terms of R². The variables with the highest VIF are precisely those related to the balance of the largest whales, suggesting that the information they bring is already, to some extent, captured by other balance variables. A reduced model, containing only the HAR components and the four statistically significant variables, obtained an R² of 0.827 and an MAE of 0.002661, outperforming the Complete model, indicating that a more parsimonious model may be preferable.

The analysis of the error by quartile of the observed real volatility in the test set for the HAR-X Balance model revealed that the mean absolute error was 0.002594 in the calmest quartile (Q1) and 0.003320 in the most volatile quartile (Q4). This means that the model tends to err approximately 28% more in periods of extreme volatility than in calm periods, which is consistent with the heteroscedasticity identified in the residuals. This characteristic is important for risk management, as it indicates that forecast accuracy may vary across different market regimes.

The heteroscedasticity of the residuals was formally confirmed by the Breusch-Pagan test, which presented an LM Statistic of 101.034 and a p-value of 0.00, in addition to an F-Statistic of 6.12 and p-value of 0.00. These results reject the null hypothesis of homoscedasticity, confirming that the variance of the residuals is dependent on the independent variables (Wooldridge, 2016). This finding validates the need to apply the Newey-West correction for standard errors, ensuring the validity of hypothesis tests and the robustness of the conclusions.

To formally test the claim of structural change in the market post-approval of spot ETFs in January 2024, a Chow Test (Chow, 1960) was applied to the Full HAR-X composition. The joint test, considering the 18 model parameters simultaneously, resulted in a Chow F-statistic of 0.72 (p=0.79), not rejecting the null hypothesis of coefficient stability. It is important to note that this result is impacted by the post-ETF sample size (721 observations for 18 variables) and should be interpreted with caution.

However, when observing the coefficients individually, a relevant movement was noted in specific variables. The coefficient for “Entry into Brokerages” lost all significance in the post-ETF period (p-value from 0.034 to 0.825), as did the one for “Net Balance in Brokerages” (p-value from 0.057 to 0.942). In contrast, the coefficient for “Total DLP Balance” remained significant and grew in magnitude (p-value from 0.003 to 0.036, with the coefficient changing from -7.17E-10 to -2.68E-09). This suggests that the post-ETF market dynamics are consistent with changes in the individual behavior of some coefficients, even if it was not confirmed as a statistically significant joint structural break.

It is crucial to clarify the terminology used. The term “whales” in this work refers to large investors, but the “on-chain” variables used do not exclusively represent strict segmentation by wallet size. Some metrics, such as “Exchange Inflow” and “Net Exchange Balance,” measure aggregate flows for the entire market, while “Total DLP Balance” segments by long-term holding behavior, not by wallet size. Only the “Whale Balance” variables by volume range represent the strictest definition of “whale” by held volume, and these did not show individual significance.

“Future volatility” refers to the predictive target of the study, i.e., the standard deviation of daily returns in the 7 days subsequent to date t. “Realized volatility” (RV), on the other hand, designates the general concept in the HAR/HAR-X literature and the autoregressive components built from past volatility. Both terms coexist in the text to describe related but distinct concepts: one is the model’s target, and the other is the autoregressive input. Furthermore, the terms “impact” and “influence” should be read as conditional predictive association to the model, not as proven direct causal relationship, as the HAR-X model identifies statistically significant correlations but does not isolate causal mechanisms nor discard alternative explanations.

In terms of practical application, the HAR-X Balance model can be integrated into institutional risk management contexts. This includes the automated daily update of 7-day volatility forecasts, the creation of visualization dashboards of predicted versus realized volatility with the model’s error history, and the development of alert triggers for when predicted volatility exceeds predefined thresholds, signaling the need for exposure review or hedging strategies. Such tools can assist institutional treasuries and fund managers in decision-making.

Despite the robustness of the results, the study has limitations. The clustering heuristics used by Glassnode to group addresses into entities may contain classification errors, as the same individual or institution may operate multiple addresses, and a single address may be shared. Furthermore, the balance ranges do not distinguish whether the holder is an individual, fund, exchange, or corporate treasury. Future work could incorporate external factors, such as macroeconomic crises, changes in interest rates, and geopolitical events, which influence the perception of risk and the return of assets like Bitcoin, to build a more accurate map of volatility.

In summary, the research results indicate that, contrary to the initial hypothesis, balance sheet metrics, especially the concentration of assets held by long-term holders, have greater predictive power over Bitcoin’s future volatility in a 7-day horizon. The HAR-X Balance model demonstrated the best explanatory capacity, with an R² of 0.826, and a mean absolute error of 0.26 percentage points, suggesting that the stability provided by large long-term accumulators acts as the main volatility buffer in the cryptoasset market, especially in the post-institutionalization scenario.

4. Conclusion

This study sought to validate whether behavioral metrics of large investors, or balance metrics, had greater predictive power over Bitcoin’s future volatility, especially in the post-market institutionalization context. It was found that, contrary to the initial hypothesis, the HAR-X Balance model demonstrated superior predictive capacity, with an R² of 0.826 on the test set, explaining 82.6% of the variance in the asset’s future volatility. It was identified that Bitcoin’s concentration in the hands of long-term holders (Total Balance DLP) acted as the main volatility buffer, showing a negative and statistically significant association. Additionally, it was observed that the entry of Bitcoins into exchanges and their seven-day variation were associated with a reduction in future volatility, while the net balance on exchanges indicated a positive association. The main practical contribution lies in offering a robust model, with a mean absolute error of 0.26 percentage points, which can be integrated into institutional risk management strategies, assisting treasuries and fund managers in forecasting Bitcoin’s 7-day volatility.

Despite the robustness of the results, the study has limitations inherent to Glassnode’s clustering heuristics, which may not precisely distinguish between holder types or entities, and to the absence of external macroeconomic factors in the model. Although the Chow test did not confirm a statistically significant joint structural break post-ETFs, a relevant shift in the individual behavior of some coefficients was observed, suggesting the need for re-evaluation with larger samples in the future and separate estimation by sub-periods. For future studies, it is recommended to incorporate external variables, such as crises and interest rates, and to use more granular Glassnode metrics for a more complete understanding of volatility dynamics. It is important to emphasize that the terms “impact” and “influence” should be interpreted as predictive associations conditioned on the model, rather than direct causal relationships.

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Article originating from the Final Course Project of the Specialization in Data Science and Analytics of the MBA USP/Esalq

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