This is a pre-print of an article published in Computational Economics. The final authenticated version is available online at: https://doi.org/10.1007/s10614-019-09879-x In this paper, we develop a very flexible and comprehensive state-space framework for modeling time series data. Our research extends the simple canonical model usually employed in the literature, into a panel-data time-varying parameters framework, combining fixed (both common and country-specific) and varying components. Under some specific circumstances, this setting can be understood as a mean-reverting panel time-series model, where the mean fixed parameter can, at the same time, include a deterministic trend. Regarding the transition equation, our structure allows for the estimation of different autoregressive alternatives, and include control instruments, whose coefficients can be set-up either common or idiosyncratic. This is particularly useful to detect asymmetries among individuals (countries) to common shocks. We develop a GAUSS code that allows for the introduction of restrictions regarding the variances of both the transition and measurement equations. Finally, we use this empirical framework to test for the Feldstein–Horioka puzzle in a 17-country panel. The results show its usefulness for solving complexities in macroeconomic empirical research.