Seasonally-Adjusted Auto-Regression of Vector Time Series
This provides a scalable solution for forecasting in domains with missing data, though it is incremental as it builds on existing time series and Gaussian process methods.
The authors tackled forecasting vector time series with missing data by developing an algorithm that models seasonal baselines and uses a Gaussian process for residuals, achieving scalability with linear memory and computation requirements.
We present a simple algorithm to forecast vector time series, that is robust against missing data, in both training and inference. It models seasonal annual, weekly, and daily baselines, and a Gaussian process for the seasonally-adjusted residuals. We develop a custom truncated eigendecomposition to fit a low-rank plus block-diagonal Gaussian kernel. Inference is performed with the Schur complement, using Tikhonov regularization to prevent overfit, and the Woodbury formula to invert sub-matrices of the kernel efficiently. Inference requires an amount of memory and computation linear in the dimension of the time series, and so the model can scale to very large datasets. We also propose a simple "greedy" grid search for automatic hyper-parameter tuning. The paper is accompanied by tsar (i.e., time series auto-regressor), a Python library that implements the algorithm.