Multitask Learning for High-dimensional Time Series

This talk introduces a novel framework for multitask learning in high-dimensional time series through hypothesis testing and data integration. The proposed procedure tests for shared structures across multiple high-dimensional factor models, determining whether they are driven by the same loading vectors up to a linear transformation. Leveraging repeated applications of singular value decomposition, the framework achieves consistent estimation of shared and non-shared loading vectors and introduces a sequential testing procedure to estimate the number of shared components. Theoretical results establish the asymptotic behavior of the test statistics and consistency. The method applies to multitask frameworks to uncover inter-individual relationships between datasets and to detecting structural changes over time in a single factor model. Applications to macroeconomic data demonstrate the framework's practical utility in revealing shared and distinct structures across datasets.