QARIMA: A Quantum Approach To Classical Time Series Analysis

2026-04-09

AI Summary

This study addresses the high computational cost and susceptibility to overfitting in traditional ARIMA models, which stem from extensive hyperparameter tuning during order identification and parameter estimation. To overcome these limitations, the authors propose a quantum-enhanced ARIMA framework that introduces quantum swap tests and delay matrices into time series modeling. Specifically, they develop quantum autocorrelation (QACF) and partial autocorrelation (QPACF) functions based on swap tests to guide model order and lag selection. Coefficients are estimated using fixed-structure variational quantum circuits (VQC-AR/VQC-MA), complemented by a lightweight quantum weak-lag refinement mechanism and information-criterion-based pruning. Evaluated across multiple environmental and industrial datasets, the approach significantly reduces out-of-sample MSE and MAPE, with its predictive superiority confirmed by Diebold–Mariano tests, while substantially lowering meta-optimization overhead.

Abstract

We present a quantum-inspired ARIMA methodology that integrates quantum-assisted lag discovery with \emph{fixed-configuration} variational quantum circuits (VQCs) for parameter estimation and weak-lag refinement. Differencing and candidate lags are identified via swap-test-driven quantum autocorrelation (QACF) and quantum partial autocorrelation (QPACF), with a delayed-matrix construction that aligns quantum projections to time-domain regressors, followed by standard information-criterion parsimony. Given the screened orders $(p,d,q)$, we retain a fixed VQC ansatz, optimizer, and training budget, preventing hyperparameter leakage, and deploy the circuit in two estimation roles: VQC-AR for autoregressive coefficients and VQC-MA for moving-average coefficients. Between screening and estimation, a lightweight VQC weak-lag refinement re-weights or prunes screened AR lags without altering $(p,d,q)$. Across environmental and industrial datasets, we perform rolling-origin evaluations against automated classical ARIMA, reporting out-of-sample mean squared error (MSE), mean absolute percentage error (MAPE), and Diebold--Mariano tests on MSE and MAE. Empirically, the seven quantum contributions -- (1) differencing selection, (2) QACF, (3) QPACF, (4) swap-test primitives with delayed-matrix construction, (5) VQC-AR, (6) VQC weak-lag refinement, and (7) VQC-MA -- collectively reduce meta-optimization overhead and make explicit where quantum effects enter order discovery, lag refinement, and AR/MA parameter estimation.

Problem

• ARIMA
• time series analysis
• model order selection
• parameter estimation
• quantum autocorrelation

Innovation

• Quantum ARIMA
• Variational Quantum Circuits
• Quantum Autocorrelation
• Swap-test
• Weak-lag Refinement