Diagnosing seasonal shifts in time series using state space models

A computationally efficient means of detecting seasonal shifts is described. The proposed diagnostic statistics are generated from the output of a smoothing algorithm associated with the Kalman filter. The method can be applied to any model for a seasonal process that can be cast in state space form. We focus on structural time series that provide a natural framework for modelling seasonal shifts. A Monte Carlo experiment establishes that approximate quantiles for the diagnostic statistics can be generated using an independence assumption.