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Stochastic and deterministic trend in state space models

Abstract In recent years state-space representations and the associated Kalman filter have had a profound impact on time series analysis and many related areas. The structural time series models are formulated in terms of unobserved components like the classical decomposition model. However, the rigidity of the classical decomposition model is avoided by allowing the components to evolve stochastically rather than deterministically. The objective of this paper is to test if the estimates obtained by the Kalman filter are able to discriminate between the slope and level when they are stochastically included to describe the trend in structural time series using state space models. The tests performed show how the information selection criteria tend to suggest the use of models with stochastic slope even in situations where it does not have a relevant presence. Unlike model selection criteria, the goodness of fit measures of the estimates prioritize mainly models with deterministic slope.