Semiparametric Time-Varying Parameters in Hierarchical Bayesian Time Series Modeling

Hierarchical Bayesian time series models are a powerful framework for analyzing intensive longitudinal data, yet their standard formulation restricts between-persondifferences in the parameters of interest to linear functions of covariates. We extend our work on within-person semiparametric DSEMs (Sørensen & McCormick, 2025) by introducing Bayesian penalized regression splines at the between-person level, enabling flexible estimation of nonlinear covariate effects on each person-specific AR(1) parameter: the mean (α), autoregressive effect (ϕ), and residual standard deviation (ψ). We further generalize this framework to measurement burst designs, proposing mixed-effects and within-person panel variants that combine intensive within-burst dynamics with population-level and individual smooth trajectories across waves. Results across simulated and real data applications demonstrate accurate recovery of nonlinear smooth functions α and ψ across all designs, with consistently weaker but still adequate recovery for ϕ due to its known identification challenges. Taken together, this work provides an initial framework for subsequent developments linking short-term dynamics with long-term change.