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.
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