\[\renewcommand{\var}{\operatorname{Var}} \renewcommand{\corr}{\operatorname{Corr}} \renewcommand{\dd}{\mathrm{d}} \renewcommand{\bb}[1]{\mathbb{#1}} \renewcommand{\vv}[1]{\boldsymbol{#1}} \renewcommand{\rv}[1]{\mathsf{#1}} \renewcommand{\vrv}[1]{\vv{\rv{#1}}} \renewcommand{\disteq}{\stackrel{d}{=}} \renewcommand{\gvn}{\mid} \renewcommand{\Ex}{\mathbb{E}} \renewcommand{\Pr}{\mathbb{P}}\]
Some useful generalisations of autoregressive (i.e. AR(1)) processes.
Linear ones are an intersting case (G. K. Grunwald, Hyndman, and Tedesco 1996; Gary K. Grunwald et al. 2000).
References
Barndorff-Nielsen, O. E. 2001. “Superposition of Ornstein-Uhlenbeck Type Processes.” Theory of Probability & Its Applications 45 (2): 175–94.
Barndorff-Nielsen, Ole Eiler, and Robert Stelzer. 2011. “Multivariate supOU Processes.” The Annals of Applied Probability 21 (1): 140–82.
Barndorff-Nielsen, Ole E., and Neil Shephard. 2001. “Non-Gaussian Ornstein–Uhlenbeck-Based Models and Some of Their Uses in Financial Economics.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2): 167–241.
Foti, Nicholas J., and Sinead A. Williamson. 2015. “A Survey of Non-Exchangeable Priors for Bayesian Nonparametric Models.” IEEE Transactions on Pattern Analysis and Machine Intelligence 37 (2): 359–71.
Griffin, J E. n.d. “Time-Dependent Stick-Breaking Processes,” 34.
Griffin, J.E. 2011. “The Ornstein–Uhlenbeck Dirichlet Process and Other Time-Varying Processes for Bayesian Nonparametric Inference.” Journal of Statistical Planning and Inference 141 (11): 3648–64.
Grunwald, G K, R J Hyndman, and L M Tedesco. 1996. “A Unified View of Linear AR(1) Models,” 26.
Grunwald, Gary K., Rob J. Hyndman, Leanna Tedesco, and Richard L. Tweedie. 2000. “Theory & Methods: Non-Gaussian Conditional Linear AR(1) Models.” Australian & New Zealand Journal of Statistics 42 (4): 479–95.
Pigorsch, Christian, and Robert Stelzer. 2009. “On the Definition, Stationary Distribution and Second Order Structure of Positive Semidefinite Ornstein–Uhlenbeck Type Processes.” Bernoulli 15 (3): 754–73.
Wolpert, Robert L. 2021. “Lecture Notes on Stationary Gamma Processes.” arXiv:2106.00087 [Math], May.
Wolpert, Robert L., and Lawrence D. Brown. 2021. “Markov Infinitely-Divisible Stationary Time-Reversible Integer-Valued Processes.” arXiv:2105.14591 [Math], May.
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