Bitcoin volatility rollercoaster

Decoding Crypto Crashes: Can Expectile Regression Tame Bitcoin's Wild Ride?

Jordan Keane in Business & Economy December 2025 • 4 min read.

"A New Approach to Understanding Cryptocurrency Returns and Managing Risk in the Digital Age."

The cryptocurrency market, particularly Bitcoin, has captured the attention of investors worldwide due to its unique characteristics and potential for high returns. However, this market is also known for extreme price volatility, speculative bubbles, and market instability, making risk management a critical concern.

Traditional methods of financial analysis often fall short when applied to cryptocurrencies due to the stylized facts, including high kurtosis, skewness, and serial correlation. Quantile regression has emerged as a valuable tool for modeling the entire distribution of returns. Expectile regression, an extension of quantile regression, offers even greater insights by characterizing the conditional distribution of a response variable and providing more informative tail expectations.

A recent research paper introduces a linear expectile hidden Markov model designed to analyze cryptocurrency time series within a risk management framework. This innovative approach focuses on extreme returns and describes their temporal evolution by introducing time-dependent coefficients that evolve according to a latent discrete homogeneous Markov chain. By leveraging the asymmetric normal distribution and an Expectation-Maximization algorithm, this model provides a powerful means of understanding and mitigating the risks associated with cryptocurrency investments.

What Are Expectile Hidden Markov Regression Models and How Do They Work?

Bitcoin volatility rollercoaster

Expectile hidden Markov regression models combine the strengths of expectile regression and hidden Markov models to provide a comprehensive analysis of time series data, particularly in the context of cryptocurrency returns. Here's a breakdown of the key components:

Expectile Regression: This method extends beyond traditional mean regression by allowing analysts to examine the entire conditional distribution of returns. Unlike quantile regression, expectiles are more sensitive to tail expectations, capturing nuances in extreme values.

Asymmetric Squared Loss Function: Expectile regression employs an asymmetric squared loss function, placing different weights on observations above and below the expectile. This is defined as: wτ(u) = u²|τ − I(u < 0)|.
Characterizing Conditional Distribution: It allows to characterize the conditional distribution of a response variable.

Hidden Markov Models (HMMs): HMMs are statistical models that describe the evolution of a system through a sequence of hidden states. In this context, the hidden states represent different market regimes, such as periods of high or low volatility. The model assumes that the observed cryptocurrency returns are influenced by these underlying states, which transition over time according to a Markov chain.

Implications for Investors and Risk Managers

The expectile hidden Markov regression model offers valuable insights for investors and risk managers seeking to navigate the complexities of the cryptocurrency market. By providing a more nuanced understanding of extreme returns and their temporal evolution, this model can help improve risk assessment, portfolio allocation, and trading strategies. As the cryptocurrency market continues to evolve, advanced analytical tools like this will be essential for making informed decisions and mitigating potential losses.

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: 10.1007/s11222-023-10377-2,

Title: Expectile Hidden Markov Regression Models For Analyzing Cryptocurrency Returns

Subject: stat.ap q-fin.rm

Authors: Beatrice Foroni, Luca Merlo, Lea Petrella

Published: 23-01-2023

Everything You Need To Know

1

What are expectile hidden Markov regression models, and how do they improve cryptocurrency analysis?

Expectile hidden Markov regression models are advanced statistical tools combining expectile regression and hidden Markov models to analyze cryptocurrency returns. Expectile regression examines the entire conditional distribution of returns, focusing on tail expectations and capturing extreme values through an asymmetric squared loss function. Hidden Markov Models describe market regimes, like high or low volatility, influencing cryptocurrency returns. This combination provides a comprehensive analysis of time series data, offering insights into risk management and market behavior beyond traditional methods.

2

How does expectile regression differ from quantile regression in analyzing cryptocurrency returns?

Expectile regression extends quantile regression by characterizing the conditional distribution of a response variable and providing more informative tail expectations. Unlike quantile regression, expectile regression is more sensitive to tail expectations, capturing nuances in extreme values. It uses an asymmetric squared loss function, defined as wτ(u) = u²|τ − I(u < 0)|, which places different weights on observations above and below the expectile, offering a more detailed understanding of extreme returns.

3

What are the benefits of using an asymmetric squared loss function in expectile regression when analyzing Bitcoin's price volatility?

The asymmetric squared loss function in expectile regression places different weights on observations above and below the expectile, defined as wτ(u) = u²|τ − I(u < 0)|. This is particularly useful for analyzing Bitcoin's price volatility because it allows the model to be more sensitive to extreme values. By weighting losses asymmetrically, the model can better capture the nuances in extreme returns, providing a more accurate assessment of risk and potential losses or gains associated with Bitcoin investments. This is key due to the market's high kurtosis, skewness, and serial correlation.

4

How can the Expectation-Maximization algorithm be applied to the expectile hidden Markov model for cryptocurrency time series analysis?

The Expectation-Maximization (EM) algorithm is used to estimate the parameters of the expectile hidden Markov model when applied to cryptocurrency time series. In the context of the expectile hidden Markov model, the EM algorithm iteratively estimates the parameters of both the expectile regression component and the hidden Markov model component. The Expectation step involves calculating the probabilities of being in each hidden state at each point in time, given the observed cryptocurrency returns and the current parameter estimates. The Maximization step involves updating the parameter estimates to maximize the likelihood of the observed data, given the state probabilities calculated in the E-step. This iterative process continues until the parameter estimates converge, providing a robust framework for analyzing cryptocurrency time series.

5

What implications does the expectile hidden Markov regression model have for investors and risk managers in the cryptocurrency market?

The expectile hidden Markov regression model offers valuable insights for investors and risk managers seeking to navigate the complexities of the cryptocurrency market. By providing a more nuanced understanding of extreme returns and their temporal evolution, this model can help improve risk assessment, portfolio allocation, and trading strategies. It enables better identification of market regimes, allowing for more informed decisions and mitigation of potential losses. As the cryptocurrency market evolves, advanced analytical tools like this are essential for making informed decisions, even though other factors, such as regulatory changes and technological advancements, also play a significant role.