Využití stavově prostorových modelů pro modelování úmrtnosti

This dissertation thesis introduces the use of state-space models for modeling and predicting of age and time specific mortality rates. The main objectives of the thesis are the following. Firstly, to assess the suitability of using state-space models for demographic mortality analysis in comparison to traditional methods of mortality rates prediction using appropriate diagnostic criteria. Subsequently, the comparison of the characteristics of state-space models and the Lee-Carter model. Finally, the theoretical assessment of other models that seek to address the biodemographic limit of the Lee-Carter model, particularly in the context of state-space models. Modeling mortality with respect to both age and time dimensions is often associated in demography with the traditionally used Lee-Carter model. The Lee-Carter model considers a constant set of parameters of age-specific mortality change for prediction, which can lead to the problem of overcoming the biodemographic limit. This paper addresses the problem of classical state-space models with a subsequent extension to generalized (exponential) state-space models. Furthermore, the theoretical background needed to obtain parameter estimates of state-space models, such as Kalman filter, Kalman smoothing, or their generalized variants in the case of generalized state-space models, are described. In this thesis, the use of generalized state-space models for the purpose of modeling and predicting of specific mortality rates is demonstrated. The main contribution of this thesis is the application of generalized state-space models for modeling and predicting mortality rates in a form that is not standardly used in demography. In particular, this is a generalized state-space Poisson model with overdispersion parameters and a generalized state-space Poisson model with dynamic parameters. As an additional contribution, a comparison of the prediction abilities of the Lee-Carter and the generalized state-space model with overdispersion parameters can be mentioned. The state-space Poisson model with overdispersion parameters led both to better results for most of the assumptions made on the random components of the Lee-Carter model, but also to slightly better results when comparing predictions of the models.