Author: Denis Avetisyan
Despite its reputation for chaos, Bitcoin‘s price and volatility can be meaningfully forecast using established time series techniques.
A new analysis demonstrates the effectiveness of ARIMA(1,1,1) and EGARCH(1,1) models for short-run Bitcoin price and volatility forecasting.
Despite the widely held belief that cryptocurrency markets defy traditional analytical approaches, this study, ‘Bitcoin Forecasting with Classical Time Series Models on Prices and Volatility’, rigorously assesses the efficacy of established time series techniques for short-run price and volatility prediction. Results demonstrate that models like ARIMA and EGARCH can meaningfully forecast Bitcoin’s dynamics, capturing both price levels and asymmetric volatility responses to market shocks. This suggests that, despite its inherent complexities, Bitcoin is not entirely immune to analysis using classical statistical frameworks. Can these findings pave the way for more robust and reliable cryptocurrency forecasting models incorporating both traditional and machine learning methodologies?
Deciphering the Rhythms of Bitcoin’s Price
Predicting Bitcoin’s price remains a formidable challenge due to its inherent volatility and the interplay of market forces. Unlike stable assets, Bitcoin’s price history fluctuates significantly, rendering traditional forecasting methods less reliable. Its decentralized nature and susceptibility to news, regulation, and investor sentiment further complicate predictive modeling.
Many time series analyses require ‘stationarity’ – consistent statistical properties over time. Financial data, including Bitcoin prices, rarely meet this criterion. Bitcoin’s non-stationarity necessitates pre-processing to stabilize the data before applying analytical models.
Calculating ‘Log Returns’ – the natural logarithm of successive price ratios – is a common practice to address non-stationarity. This converts the price series into percentage changes, often exhibiting more stable properties. Log returns are preferred over simple percentages due to their mathematical advantages in certain models.
Though chaotic in appearance, Bitcoin’s price reveals a hidden order when viewed through transformed data – a subtle harmony emerging from the noise.
Modeling Price Dynamics with ARIMA and SARIMA
The Autoregressive Integrated Moving Average (ARIMA) model is a widely used statistical method for time series forecasting. It leverages $Autocorrelation$ – the correlation between a time series’ current and past values – to predict future data points. Careful selection of the model’s parameters – (p, d, q) – representing autoregression, differencing, and the moving average, is crucial for accurate forecasting.
Time series data often exhibit $non-stationarity$, requiring $Differencing$ – calculating the difference between consecutive observations – to convert a non-stationary series into a stationary one, fulfilling a key ARIMA assumption. Stationarity ensures consistent model parameters and improves forecast reliability.
While the Seasonal ARIMA (SARIMA) model extends the basic framework by incorporating seasonal components, evaluation reveals that the ARIMA(1,1,1) model outperforms it, exhibiting lower Mean Absolute Error and Root Mean Squared Error. This suggests that observed patterns are adequately captured by the non-seasonal model, and seasonal components do not improve predictive accuracy.
Capturing Volatility’s Clustering Effect
Bitcoin prices are characterized by ‘Volatility Clustering’, where periods of high and low volatility tend to cluster together. This deviation from traditional model assumptions necessitates techniques capable of capturing these dynamic shifts in price fluctuation.
Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models are specifically designed to address volatility clustering. These models allow the conditional variance of the price series to change over time, providing a more realistic representation of Bitcoin’s price dynamics. The Exponential GARCH (EGARCH) model extends this by allowing asymmetric responses to positive and negative shocks.
Analysis demonstrates that the EGARCH(1,1) model exhibits lower Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values compared to the GARCH(1,1) model, indicating a statistically superior fit and more accurate capture of Bitcoin’s conditional volatility.
Balancing Model Complexity and Accuracy
Model selection for Bitcoin price forecasting requires balancing model fit and complexity. Metrics such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) evaluate this trade-off, penalizing complexity while rewarding fit, ensuring good generalization to unseen data.
Accuracy is quantified using forecasting metrics like Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE), providing a measure of prediction error magnitude and allowing for comparison between models. Comparative analysis reveals that certain configurations consistently outperform others in capturing Bitcoin’s price dynamics.
The ARIMA(1,1,1) model demonstrates an AR(1) coefficient of -0.1203 and a MA(1) coefficient of 0.4103, suggesting a slight tendency for price changes to reverse direction, but also carry over into the following day. Furthermore, the EGARCH(1,1) model reveals an $α_1$ value of 0.4407 and a $β_1$ value of 0.9054, quantifying the impact of short-run shocks and demonstrating high persistence of volatility. The interplay of these parameters hints that the true shape of volatility lies in the subtleties of its design.
The study’s success in applying classical time series models to the notoriously volatile Bitcoin market demonstrates a fundamental principle: elegance in methodology can reveal underlying order even within apparent chaos. This echoes Marie Curie’s sentiment: “Nothing in life is to be feared, it is only to be understood.” The researchers, by focusing on stationarity and employing models like ARIMA(1,1,1) and EGARCH(1,1), didn’t attempt to predict the unpredictable; instead, they sought to understand the patterns within the volatility. This approach, prioritizing clarity and a deep grasp of the data’s characteristics, allowed for meaningful short-run forecasts, affirming that rigorous analysis, even with established techniques, can illuminate complex systems.
The Road Ahead
The persistence of predictive power in classical time series models – even for an asset seemingly designed to defy prediction – suggests a fundamental truth: markets, however novel their packaging, remain susceptible to the echoes of their own history. The observed efficacy of ARIMA and EGARCH is not necessarily a statement about Bitcoin, but a reminder of the enduring utility of elegantly simple tools. Yet, a certain discomfort lingers. These models capture short-run behavior; they do not, and cannot, address the underlying question of Bitcoin’s long-term value proposition – or lack thereof. Consistency is empathy; a model that fails to account for the evolving narrative surrounding an asset is, ultimately, a fragile approximation.
Future work must move beyond mere forecasting accuracy. The focus should shift toward understanding why these models function, and, more importantly, identifying the conditions under which they will fail. Consideration of agent-based modeling, incorporating behavioral heuristics and network effects, could offer a richer, if more complex, picture. The goal isn’t to achieve perfect prediction – a fool’s errand – but to map the boundaries of predictability, acknowledging that beauty does not distract, it guides attention.
Finally, the study of Bitcoin volatility deserves continued attention. The observed volatility clustering, while captured by EGARCH, warrants investigation into the potential influence of external shocks – regulatory announcements, technological disruptions, or even shifts in broader macroeconomic sentiment. Perhaps the most challenging task will be to discern whether these shocks represent truly exogenous events, or merely the inevitable consequence of an asset built on foundations of radical decentralization and speculative fervor.
Original article: https://arxiv.org/pdf/2511.06224.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-11-12 02:05