Title: Seasonally-Adjusted Auto-Regression of Vector Time Series Show Chinese title

Title: 季节性调整向量时间序列的自回归模型

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. Show Chinese abstract

Abstract: 我们提出了一种简单的算法，用于预测向量时间序列，并且该算法在训练和推理过程中都对缺失数据具有鲁棒性。 它对季节性的年、周和日基线进行建模，并对经过季节调整的残差采用高斯过程。 我们开发了一种自定义截断特征分解方法，以拟合低秩加块对角高斯核。 推理使用Schur补，并通过Tikhonov正则化防止过拟合，同时利用Woodbury公式高效地求解核矩阵的子矩阵逆。 推理所需的内存和计算量与时间序列维度呈线性关系，因此该模型可以扩展到非常大的数据集。 我们还提出了一个简单的“贪心”网格搜索方法，用于自动超参数调节。 本文附带了一个名为tsar（即时间序列自回归器）的Python库，该库实现了该算法。