We present a novel approach to multivariate time series forecasting by framing it as a multi-task learning problem. We propose an optimization strategy that enhances single-channel predictions by leveraging information across multiple channels. Our framework offers a closed-form solution for linear models and connects forecasting performance to key statistical properties using advanced analytical tools. Empirical results on both synthetic and real-world datasets demonstrate that integrating our method into training loss functions significantly improves univariate models by effectively utilizing multivariate data within a multi-task learning framework.