Surreal illustration of crypto market volatility with rough waves and long swells.

Decoding Crypto Volatility: Is Roughness the New Long Memory?

Kai Mendoza in Business & Economy September 2025 • 4 min read.

"Unraveling the short-term and long-term dynamics of cryptocurrency market fluctuations using advanced statistical methods."

The cryptocurrency market is known for its extreme volatility, making it a fascinating yet challenging arena for investors and economists alike. Understanding the nature of this volatility is crucial for risk management, investment strategies, and even regulatory policies. Recent research has begun to question traditional models, suggesting that the dynamics of crypto volatility may be more complex than previously thought.

One emerging concept is that of 'rough volatility,' which posits that the paths of volatility are more erratic than standard models assume. This contrasts with the idea of 'long memory,' where past volatility has a persistent influence on future levels. A recent academic paper delves into these competing ideas, using sophisticated statistical techniques to dissect the intricacies of crypto market fluctuations.

This article aims to break down the key findings of this research, explaining how a method called 'composite likelihood estimation' helps to disentangle the short-term 'roughness' and long-term memory effects in crypto volatility. We’ll explore what this means for understanding market behavior and potentially predicting future swings.

What's the Difference Between Roughness and Long Memory in Volatility?

Surreal illustration of crypto market volatility with rough waves and long swells.

To understand the research, we need to define two important concepts: roughness and long memory. Think of volatility as the 'speed' at which prices change. Roughness refers to how choppy or uneven that speed is in the short term. A rough volatility process would show wild, unpredictable swings over short periods.

Long memory, on the other hand, describes the persistence of volatility over longer time horizons. If volatility has long memory, then periods of high volatility tend to be followed by more high volatility, and vice versa. The key is that the influence of past volatility levels fades away slowly over time.

Roughness: Short-term, erratic changes in volatility.
Long Memory: Persistent influence of past volatility on future levels.

Traditional models often struggle to capture both of these features simultaneously. The challenge is that a process might appear rough in the short term simply because of random noise, without any true long-term dependence. Or, a model might capture long memory but fail to account for the sudden, sharp spikes in volatility that are common in crypto markets.

The Future of Volatility Modeling

The study underscores the need for models that can flexibly capture both the short-term and long-term dynamics of volatility. By disentangling roughness and long memory, researchers and practitioners can gain a more nuanced understanding of market behavior, leading to better risk management and investment decisions. As the crypto market continues to evolve, these advanced statistical techniques will likely play an increasingly important role in navigating its inherent uncertainty.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2403.12653,

Title: Composite Likelihood Estimation Of Stationary Gaussian Processes With A View Toward Stochastic Volatility

Subject: econ.em q-fin.mf

Authors: Mikkel Bennedsen, Kim Christensen, Peter Christensen

Published: 19-03-2024

Everything You Need To Know

What is 'roughness' in the context of crypto volatility, and how does it differ from 'long memory'?

In the realm of crypto volatility, 'roughness' describes the short-term erratic changes in the speed at which prices change, indicating wild and unpredictable swings over brief periods. This contrasts with 'long memory,' which refers to the persistent influence of past volatility on future levels over extended time horizons. If volatility exhibits 'long memory,' periods of high volatility tend to be followed by more high volatility, and vice versa, with past levels fading slowly over time. Essentially, 'roughness' focuses on immediate, choppy movements, while 'long memory' highlights the lasting impact of past volatility on the market's future behavior.

How can 'composite likelihood estimation' help in understanding crypto market fluctuations?

‘Composite likelihood estimation’ is a sophisticated statistical method used to dissect the intricacies of crypto market fluctuations by disentangling the short-term 'roughness' and long-term 'long memory' effects in crypto volatility. It helps researchers and practitioners gain a more nuanced understanding of market behavior. This allows for the development of models that more accurately capture both short-term and long-term dynamics, improving risk management and investment decisions in the volatile crypto market.

Why are traditional volatility models insufficient for the cryptocurrency market?

Traditional models often struggle to capture both the short-term 'roughness' and long-term 'long memory' features of the crypto market simultaneously. These models may fail to account for the sudden, sharp spikes in volatility common in crypto, or they may mistake random noise for true long-term dependence. The challenge lies in accurately representing the complex interplay of erratic short-term changes ('roughness') and the persistent influence of past volatility ('long memory') that define the crypto market.

What are the implications of understanding both 'roughness' and 'long memory' for investors?

Understanding both 'roughness' and 'long memory' in crypto volatility offers investors a more nuanced understanding of market behavior, leading to better risk management and investment decisions. Recognizing 'roughness' allows investors to anticipate and manage the impact of sudden, unpredictable swings. Simultaneously, understanding 'long memory' helps in predicting future volatility based on past trends. This combined insight enables investors to develop more informed strategies, navigate market uncertainty effectively, and potentially capitalize on emerging opportunities.

How might advanced statistical techniques influence the future of volatility modeling in the crypto market?

Advanced statistical techniques, like 'composite likelihood estimation,' will likely play an increasingly important role in navigating the inherent uncertainty of the crypto market. By disentangling 'roughness' and 'long memory', researchers and practitioners can develop more accurate models that reflect the true dynamics of crypto volatility. These improved models will lead to enhanced risk management, more informed investment strategies, and a deeper understanding of the market's behavior. As the crypto market continues to evolve, the ability to capture both short-term and long-term volatility patterns will become even more critical for success.