Volatility time series modeling by single-qubit quantum circuit learning

TL;DR

This paper demonstrates that single-qubit quantum circuit learning can effectively model and preserve key statistical properties of volatility time series, including asymmetry, anti-persistence, and multifractality.

Contribution

It introduces a novel application of quantum machine learning to financial time series modeling, capturing complex volatility dynamics.

Findings

QCL preserves negative return-volatility correlation.

Predicted series exhibit anti-persistent behavior.

Multifractal structure is retained in predictions.

Abstract

We employ single-qubit quantum circuit learning (QCL) to model the dynamics of volatility time series. To assess its effectiveness, we generate synthetic data using the Rational GARCH model, which is specifically designed to capture volatility asymmetry. Our results show that QCL-based volatility predictions preserve the negative return-volatility correlation, a hallmark of asymmetric volatility dynamics. Moreover, analysis of the Hurst exponent and multifractal characteristics indicates that the predicted series, like the original synthetic data, exhibits anti-persistent behavior and retains its multifractal structure.