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### Título

INDIRECT ESTIMATION FOR $\ALPHA$-STABLE TIME-VARYING AR(1) PROCESSES

### Resumo

Locally stationary process is the class of processes that are approximately stationary in a neighborhood of each time point but its structure, such as covariances and parameters, gradually changes throughout the time period. We consider the case of time varying AR(1) (tvAR(1)) processes with $\alpha$-stable innovations. The $\alpha$-stable family of distributions is a generalization of the Gaussian distribution, which includes the possibility of handling asymmetry and thicker tails. Its estimation is difficult since its density function does not have a closed-form. Therefore, the usual estimation methods do not work. We propose the indirect inference, which is an intensive computationally simulation based method, to estimate $\alpha$-stable tvAR(1). In this paper, we obtain some theoretical results of the process and present simulation study of the estimation method.

### Palavras-chave

locally stationary process; stable distributions; indirect estimation

### Área

Séries Temporais e Econometria

### Autores

Shu Wei Chou Chen, Pedro Alberto Morettin