This paper introduces MultiDimSPCI, a sequential conformal prediction method for multivariate time series. Unlike traditional univariate conformal prediction methods, MultiDimSPCI constructs ellipsoidal prediction regions that capture the correlation between multiple dimensions of the time series. The method is designed to maintain valid coverage while producing smaller prediction regions than existing baselines. Theoretical analysis shows that MultiDimSPCI provides finite-sample high-probability bounds on the conditional coverage gap without assuming data exchangeability. Empirical results on both simulated and real-world multivariate time series demonstrate that MultiDimSPCI achieves valid coverage with significantly smaller prediction regions compared to other methods, including copula-based and probabilistic forecasting approaches. The method uses an ellipsoidal uncertainty set, which is adaptively calibrated during test time, and leverages sequential conformal inference to account for temporal dependencies in the data. The paper also discusses the benefits of using ellipsoidal prediction sets over hyper-rectangular ones, and highlights the advantages of the proposed method in capturing complex dependencies between time series dimensions. The results show that MultiDimSPCI outperforms existing methods in terms of both coverage and prediction region size, making it a promising approach for uncertainty quantification in multivariate time series forecasting.This paper introduces MultiDimSPCI, a sequential conformal prediction method for multivariate time series. Unlike traditional univariate conformal prediction methods, MultiDimSPCI constructs ellipsoidal prediction regions that capture the correlation between multiple dimensions of the time series. The method is designed to maintain valid coverage while producing smaller prediction regions than existing baselines. Theoretical analysis shows that MultiDimSPCI provides finite-sample high-probability bounds on the conditional coverage gap without assuming data exchangeability. Empirical results on both simulated and real-world multivariate time series demonstrate that MultiDimSPCI achieves valid coverage with significantly smaller prediction regions compared to other methods, including copula-based and probabilistic forecasting approaches. The method uses an ellipsoidal uncertainty set, which is adaptively calibrated during test time, and leverages sequential conformal inference to account for temporal dependencies in the data. The paper also discusses the benefits of using ellipsoidal prediction sets over hyper-rectangular ones, and highlights the advantages of the proposed method in capturing complex dependencies between time series dimensions. The results show that MultiDimSPCI outperforms existing methods in terms of both coverage and prediction region size, making it a promising approach for uncertainty quantification in multivariate time series forecasting.