Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

翻译：针对多变量时间序列的联合预测集应在控制单事件的同时适应跨坐标依赖性。本文研究了滤波共形椭球方法：固定状态空间滤波器生成单步预测均值与协方差，并采用分裂共形校准处理所得的马氏距离评分。滤波器用于选择椭球形状，共形校准则确定标量半径，从而在无需依赖高斯尾部概率保证覆盖率的条件下，利用学习到的预测协方差提升构建效果。核心难点在于滤波评分具有依赖性，且学习型递归滤波器未必能压缩其原始隐藏状态。为此，我们分析了可观测量预测律商中的压缩性——该商可识别产生相同未来高斯律序列的隐藏状态。在稳定贝叶斯高斯投影滤波器、协方差界及有限时域可观测性费舍尔条件下，较小的超额高斯负对数似然意味着学习发射律的压缩性。结合阈值自协方差包络，可获得依赖条件下滤波分裂共形预测的切比雪夫型近似覆盖界；更优的伯恩斯坦型界需要额外的几何混合浓度假设。在高斯预言机可实现性假设下，我们还在条件有效高斯椭球规则类中获得了近预言机对数体积比较结果。我们采用对角加低秩协方差的GCN-GRU滤波器实例化该框架。在中等规模图原生交通基准（METRLA-$20$和PEMSBAY-$50$）上，学习型滤波器生成的期望水平椭球比静态协方差及非滤波基线更尖锐；在全图规模及非图原生数据集上，因子与连接函数基线表现更优。