QARIMA: A Quantum Approach To Classical Time Series Analysis

Abstract:We present QARIMA, a quantum state-similarity-based reconstruction of the classical ARIMA modelling pipeline. Rather than using a quantum circuit as a standalone forecaster, QARIMA preserves ARIMA's interpretable forecasting structure while reformulating its core building blocks through analogous quantum-compatible modules. The framework integrates quantum differencing assessment, QACF/QPACF lag discovery, compact-swap-test state projection, swap-test/VQC-based AR and MA coefficient estimation, and weak-lag refinement within a single ARIMA forecasting workflow. QACF and QPACF serve the functional roles of ACF and PACF for MA and AR lag discovery, but construct lag relevance through quantum measurement geometry rather than direct classical correlation. Given screened candidate orders $(p,d,q)$, AR and MA coefficients are estimated through state-alignment losses incorporating cosine alignment, entropy regularization, phase correction, and norm control. We evaluate QARIMA across environmental, climatic, industrial, and weather time-series datasets using rolling-origin out-of-sample testing against automated classical ARIMA baselines, with performance assessed through MSE, MAPE, and Diebold--Mariano tests. The results show that quantum state-similarity modules can produce competitive and, in several cases, improved forecasting behaviour while preserving ARIMA's transparency, modularity, and interpretability. QARIMA therefore establishes a distinct pathway for quantum-enhanced statistical forecasting: its modules remain functionally analogous to classical ARIMA subroutines, but are not algebraic replicas; they serve the same modelling roles through state overlap, projection, and measurement-driven parameter estimation.

Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2604.08277 [quant-ph]

(or arXiv:2604.08277v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.08277 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.