QARIMA: A Quantum Approach To Classical Time Series Analysis
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911579994324992 |
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| author | Mohanty, Nishikanta Behera, Bikash K. Mukherjee, Badshah Dash, Pravat |
| author_facet | Mohanty, Nishikanta Behera, Bikash K. Mukherjee, Badshah Dash, Pravat |
| contents | We present a quantum-inspired ARIMA methodology that integrates quantum-assisted lag discovery with 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | QARIMA: A Quantum Approach To Classical Time Series Analysis Mohanty, Nishikanta Behera, Bikash K. Mukherjee, Badshah Dash, Pravat Quantum Physics Artificial Intelligence Machine Learning We present a quantum-inspired ARIMA methodology that integrates quantum-assisted lag discovery with 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. |
| title | QARIMA: A Quantum Approach To Classical Time Series Analysis |
| topic | Quantum Physics Artificial Intelligence Machine Learning |
| url | https://arxiv.org/abs/2604.08277 |