Inuência do número de partículas na estimação de parâmetros via máxima verossimilhança em modelos de espaço de estados

Abstract

State space models are widely used to model various problems in the areas of economics and biology, so inferences, such as parameter estimation, for this class of models are important. For these cases, the algorithms of class of particle lters are able to solve questions related to non-linear and non-Gaussian models. Poyiadjis et al. (2011) proposes two versions of algorithms of this class for the parameter estimation in state space models. One version has linear computational complexity in the number of particles and the variance of the estimates that increases quadratically over time. The other one has a quadratic computational cost and variance of the estimates increases linear through time. Based on this results, Nemeth et al.(2016) presents a new version, using the kernel density methods and Rao-Blackwellisation, in which the variance of estimates and the computational complexity are linear. Therefore, in this paper, we analyze the inuence of the number of particles in this last version and we obtain an ideal number of particles to be used for the parameter estimation in state space models, for example, autoregressive model, stochastic volatility model, and Poisson model. Finally, we use a bootstrap lter version to compare with the model shown by Nemeth et al. (2016)