We introduce the tensor auto-regressive (TAR) model for modeling time series data, which is found to be robust to model misspecification, seasonality, and nonlinear trends. We develop a parameter estimation algorithm for the proposed model by using the 𝑡-product, which allows us to model a three-dimensional block of parameters. We use the fast Fourier transform, which allows for efficient and parallelizable computation. We use a combination of simulated data and an empirical application to: (i) validate the model, including seasonal and geometric trends, model misspecification analysis, and bootstrapping to compute standard errors; (ii) present model selection results; and (iii) demonstrate the performance of the proposed model against benchmarking and competitive forecasting methods. Our results indicate that our model performs well against comparable methods and is robust and computationally efficient.

中文翻译：

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张量自回归模型

我们引入了用于建模时间序列数据的张量自回归 (TAR) 模型，该模型被发现对于建模错误规范、季节性和非线性趋势具有鲁棒性。我们通过使用 𝑡 乘积为所提出的模型开发了一种参数估计算法，它允许我们对参数的三维块进行建模。我们使用快速傅立叶变换，它允许高效且可并行的计算。我们结合使用模拟数据和经验应用来：(i) 验证模型，包括季节性和几何趋势、模型错误指定分析和引导以计算标准误差；(ii) 当前模型选择结果；(iii) 对照基准和竞争性预测方法证明所提出模型的性能。