Model Selection Problems in State Space Modelling

variable selection State space models are a widely used tool in time series analysis to deal with processes which gradually change over time. Parameter estimation for these models is studied by many authors, see e.g. Durbin and Koopman (2000) and Frühwirth-Schnatter (1994) for normal state space models, Durbin and Koopman (2001) and Frühwirth-Schnatter and Wagner (to appear) for state space modelling of count data. Relatively little, however has been done to deal with model uncertainty issues, the main reason being that model selection for state space models in general leads to a non-regular statistical testing problem. For an applied statistician, choosing an appropriate model from a class of candidate models is a fundamental data analysis task. For a state space model it would be of interest to learn from the data, which components of the state vector actually are dynamic and which components of the state vector should be included in the model. In the prominent basic structural model e.g., the state vector consists of the level µt, a trend component at and a seasonal component st, each of them being dynamic, i.e. for monthly dat