Low Rank Forecasting

2021/01/29 by Shane Barratt, Barratt, Shane, Yining Dong +3
Computer Science · Decision Sciences · Engineering · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Forecasting Techniques and Applications #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2101.12414

openalex publication_date 2021/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of forecasting multiple values of the future of a vector time series, using some past values. This problem, and related ones such as one-step-ahead prediction, have a very long history, and there are a number of well-known methods for it, including vector auto-regressive models, state-space methods, multi-task regression, and others. Our focus is on low rank forecasters, which break forecasting up into two steps: estimating a vector that can be interpreted as a latent state, given the past, and then estimating the future values of the time series, given the latent state estimate. We introduce the concept of forecast consistency, which means that the estimates of the same value made at different times are consistent. We formulate the forecasting problem in general form, and focus on linear forecasters, for which we propose a formulation that can be solved via convex optimization. We describe a number of extensions and variations, including nonlinear forecasters, data weighting, the inclusion of auxiliary data, and additional objective terms. We illustrate our methods with several examples.

Citations

• The Approximation of One Matrix by Another of Lower Rank
• On the limited memory BFGS method for large scale optimization
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