Placeholder. idk really, but Cosma Shalizi has opinions on unifying some interesting ideas in this area using chains with complete connections. Maybe related (?) predictive processing as a model of the mind.
Blasques, F., S. J. Koopman, and A. Lucas. 2015. “Information-Theoretic Optimality of Observation-Driven Time Series Models for Continuous Responses.” Biometrika 102 (2): 325–43. https://doi.org/10.1093/biomet/asu076.
Cox, D. R., Gudmundur Gudmundsson, Georg Lindgren, Lennart Bondesson, Erik Harsaae, Petter Laake, Katarina Juselius, and Steffen L. Lauritzen. 1981. “Statistical Analysis of Time Series: Some Recent Developments [with Discussion and Reply].” Scandinavian Journal of Statistics 8 (2): 93–115. http://www.jstor.org/stable/4615819.
Davis, Richard A., and Heng Liu. 2012. “Theory and Inference for a Class of Observation-Driven Models with Application to Time Series of Counts.” arXiv:1204.3915 [math, Stat], April. http://arxiv.org/abs/1204.3915.
Douc, Randal, François Roueff, and Tepmony Sim. 2015. “Handy Sufficient Conditions for the Convergence of the Maximum Likelihood Estimator in Observation-Driven Models.” arXiv:1506.01831 [math, Stat], June. http://arxiv.org/abs/1506.01831.
Fernández, Roberto, and Grégory Maillard. n.d. “Chains with Complete Connections: General Theory, Uniqueness, Loss of Memory and Mixing Properties.” Journal of Statistical Physics 118 (3-4): 555–88. https://doi.org/10.1007/s10955-004-8821-5.