Sequentially adaptive Bayesian learning for a nonlinear model of the secular and cyclical behavior of US real GDP

There is a one-to-one mapping between the conventional time series parameters of a third-order autoregression and the more interpretable parameters of secular half-life, cyclical half-life and cycle period. The latter parameterization is better suited to interpretation of results using both Bayesian and maximum likelihood methods and to expression of a substantive prior distribution using Bayesian methods. The paper demonstrates how to approach both problems using the sequentially adaptive Bayesian learning algorithm and sequentially adaptive Bayesian learning algorithm (SABL) software, which eliminates virtually of the substantial technical overhead required in conventional approaches and produces results quickly and reliably. The work utilizes methodological innovations in SABL including optimization of irregular and multimodal functions and production of the conventional maximum likelihood asymptotic variance matrix as a by-product.