Probabilistic reduced-dimensional vector autoregressive modeling with oblique projections

In this paper, we propose a probabilistic reduced-dimensional vector autoregressive model to extract low-dimensional dynamics from large dimensional noisy data. The model partitions the measurement space into a subspace of reduced-dimensional dynamics and a complementary noise subspace, where the dynamic and static noise sources can be correlated contemporaneously. An oblique projection is required to achieve a partition for the best predictability. A maximum likelihood framework is developed with instrumental variables interpretation and refinement to achieve minimum covariance of the latent prediction errors, yielding dynamic latent variables with a non-increasing order of predictability and an explicit latent dynamic model. The superior performance and efficiency of the proposed approach are demonstrated using datasets from a simulated system and an industrial process.