Placeholder. How to select models when you can’t simply cross-validate away your pain. Close to what learning theory for dependent data does.
Rob Hyndman explains how to cross-validate time series models that use only the lagged observations. Cosma Shalizi mentions the sample splitting problem for time series for post-selection inference and has supervised students to do some work with it, notably (Lunde 2019).
Alquier, Pierre, and Olivier Wintenberger. 2012. “Model Selection for Weakly Dependent Time Series Forecasting.” Bernoulli. http://arxiv.org/abs/0902.2924.
Bergmeir, Christoph, Rob J. Hyndman, and Bonsoo Koo. 2018. “A Note on the Validity of Cross-Validation for Evaluating Autoregressive Time Series Prediction.” Computational Statistics & Data Analysis 120 (April): 70–83. https://doi.org/10.1016/j.csda.2017.11.003.
Broersen, Petrus MT. 2006. Automatic Autocorrelation and Spectral Analysis. Secaucus, NJ, USA: Springer. http://dsp-book.narod.ru/AASA.pdf.
Ding, J., V. Tarokh, and Y. Yang. 2018. “Model Selection Techniques: An Overview.” IEEE Signal Processing Magazine 35 (6): 16–34. https://doi.org/10.1109/MSP.2018.2867638.
Lunde, Robert. 2019. “Sample Splitting and Weak Assumption Inference for Time Series,” February. http://arxiv.org/abs/1902.07425.
Lunde, Robert, and Cosma Rohilla Shalizi. 2017. “Bootstrapping Generalization Error Bounds for Time Series,” November. http://arxiv.org/abs/1711.02834.