Seasonally-Adjusted Auto-Regression of Vector Time Series

TL;DR

This paper introduces a robust, scalable algorithm for forecasting vector time series that accounts for seasonal patterns and residuals, with an accompanying Python library for practical implementation.

Contribution

It presents a novel seasonal-adjusted auto-regression method with efficient inference techniques and automatic hyper-parameter tuning, suitable for large datasets.

Findings

Robust forecasting with missing data handling.

Efficient inference scales linearly with data dimension.

Open-source Python library implementation.

Abstract

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.