A Dynamic Holiday-Loading Model for Weekly Time Series with Evolving Annual Effects

Thomas M. Menino Convention & Exhibition Center 

Weekly economic and administrative time series often contain localized calendar effects that are not well represented by smooth annual seasonality. We propose a dynamic holiday-loading model that separates the geometry of a recurring calendar effect from its year-specific magnitude. The geometry is represented by compactly supported loading functions that describe the timing, duration, and shape of each holiday response, while the corresponding annual intensities evolve across years through parsimonious stochastic models. The framework accommodates multiple calendar effects, including effects whose windows overlap in time, and reduces to a standard dynamic regression model once the loading functions are fixed. Estimation is based on a marginal Gaussian likelihood profiled over candidate loading windows. Simulation experiments are designed to evaluate bandwidth recovery for single and multiple holiday effects, sensitivity to kernel misspecification, and the impact of overlapping holiday windows. The method is applied to weekly U.S. Business Formation Statistics data, where it identifies distinct turn-of-year and Thanksgiving effects that are not captured by a smooth seasonal baseline.

Weekly time series

Dynamic holiday effects

Calendar adjustment

Profile likelihood