Dynamic Regression Models for Time-Ordered Functional Data

For time-ordered functional data, an important yet challenging task is to forecast observations with uncertainty quantification. Scalar predictors are often observed concurrently data and provide valuable information about the dynamics of time series. We develop a fully Bayesian framework for dynamic regression, which employs scalar model time-evolution data. Functional within-curve dependence modeled using unknown basis functions, learned from The provides substantial dimension reduction, essential scalable computing, may incorporate prior knowledge such as smoothness or periodicity. specified time-varying parameter regression in effects evolve over time. To guard against overfitting, we design shrinkage priors that regularize irrelevant shrink toward time-invariance. Simulation studies decisively confirm utility these modeling choices. Posterior inference available via customized Gibbs sampler, offers unrivaled scalability regression. methodology applied yield curves macroeconomic predictors, demonstrates exceptional forecasting accuracy quantification span four decades.