High\text{--}resolution scientific data, such as geomagnetic index streams, often exhibit complex temporal dependencies that can be modeled through functional data analysis. Conventional functional time series (FTS) methods typically partition continuous processes into non-overlapping segments, which artificially fragments temporal continuity and can limit estimation efficiency and stability. This is particularly evident in geomagnetic time series prediction due to their noisy, sudden, and large\text{--}scale changes. This study presents a robust multivariate FTS forecasting framework for multi\text{--}dimensional time series with inter\text{--}series correlations and the existence of exogenous predictors. We introduce an overlapping rolling\text{--}window scheme that preserves temporal coherence and mitigates boundary information loss, thereby enriching the effective sample size for a more efficient and stable estimation. We integrate functional principal component analysis for dimension reduction with a vector autoregressive model with exogenous inputs to capture latent dynamics across correlated series. We also construct computationally efficient conformal prediction intervals for uncertainty quantification. The framework is motivated by and applied to the simultaneous forecasting of five critical geomagnetic indices, Kp, Dst, SYM\text{--}H, SME, and SMR, using solar wind parameters as predictors. Empirical results show that this approach outperforms state\text{--}of\text{--}the\text{--}art machine learning baselines, extends forecast horizons to 6\text{--}24 hours, and provides calibrated uncertainty bounds.

翻译：高分辨率科学数据（如地磁指数序列）常表现出复杂的时间依赖性，可通过函数数据分析进行建模。传统函数时间序列方法通常将连续过程划分为非重叠片段，人为割裂时间连续性，可能导致估计效率与稳定性受限——这一问题在地磁时间序列预测中尤为突出，因其数据存在噪声大、突变多、变化尺度大等特点。本文提出一种稳健的多元函数时间序列预测框架，适用于具有序列间相关性和外生预测变量的多维数据。我们引入重叠滚动窗口方案，保留时间连贯性并减少边界信息损失，从而增加有效样本量以提高估计效率与稳定性。通过整合函数主成分分析降维与外生输入向量自回归模型，捕获相关序列间的潜在动态特征，并构建计算高效的一致性预测区间以实现不确定性量化。该框架以太阳风参数为预测变量，应用于Kp、Dst、SYM-H、SME与SMR五个关键地磁指数的同步预测。实验结果表明，该方法优于当前最先进的机器学习基线，可扩展预测时域至6-24小时，并提供校准后的不确定性边界。