Most model selection methods for time series models with many predictors are devised for the stationary processes. We consider the problem of selecting higher-order autoregressive (AR) models whose integration orders can be positive or zero, and hence both stationary and non-stationary cases are included. Combining the strengths of AIC and BIC, we propose a two-stage information criterion (TSIC), and show that TSIC is asymptotically efficient in predicting integrated AR models when the underlying AR coefficients satisfy a wide range of conditions. We also conduct a simulation study to compare the performance of AIC, HQIC, BIC, TSIC, Lasso, the adaptive Lasso and the bridge criterion. Our study reveals that TSIC performs favorably compared to other methods in various scenarios.

中文翻译：

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可能是无限次非平稳时间序列的订单选择

对于具有多个预测变量的时间序列模型，大多数模型选择方法都是针对平稳过程而设计的。我们考虑选择积分阶次可以为正或为零的高阶自回归（AR）模型的问题，因此包括稳态和非稳态情况。结合AIC和BIC的优势，我们提出了一个两阶段信息标准（TSIC），并证明了当基础AR系数满足各种条件时，TSIC在渐进式预测集成AR模型方面是有效的。我们还进行了仿真研究，以比较AIC，HQIC，BIC，TSIC，套索，自适应套索和桥梁标准的性能。我们的研究表明，在各种情况下，TSIC的性能优于其他方法。