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.

翻译：我们提出一种受量子启发的ARIMA方法论，该方法将量子辅助的滞后发现与固定配置变分量子电路（VQCs）相结合，用于参数估计和弱滞后优化。通过交换测试驱动的量子自相关函数（QACF）和量子偏自相关函数（QPACF）识别差分阶数和候选滞后项，采用延迟矩阵构造将量子投影与时域回归变量对齐，并基于标准信息准则进行简约性筛选。在确定模型阶数$(p,d,q)$后，我们保留固定的VQC线路结构、优化器和训练预算以防止超参数泄露，并将该电路部署于两种估计任务：VQC-AR用于自回归系数估计，VQC-MA用于滑动平均系数估计。在筛选与估计之间，通过轻量级VQC弱滞后优化过程，在不改变$(p,d,q)$的前提下对筛选出的AR滞后项进行权重调整或剪枝。基于环境和工业数据集，我们以滚动时间原点评估方式与自动经典ARIMA方法进行对比，报告样本外均方误差（MSE）、平均绝对百分比误差（MAPE），并通过Diebold-Mariano检验对MSE和MAE进行统计比较。实验表明，七项量子贡献——(1)差分阶数选择、(2)QACF、(3)QPACF、(4)基于延迟矩阵构造的交换测试基元、(5)VQC-AR、(6)VQC弱滞后优化、(7)VQC-MA——共同减少了元优化开销，并明确了量子效应在阶数发现、滞后优化及AR/MA参数估计中的具体介入环节。