In the thesis we present a novel solution of Bayesian filtering in autoregression model with Laplace distributed innovations. Estimation of regression models with leptokurtically distributed innovations has been studied before in a Bayesian framework [\cite{Zellner:76}], [\cite{Congdon:06}]. Compared to previously conducted studies, the method described in this article leads to an exact solution for density specifying the posterior distribution of parameters. Such a solution was previously known only for a very limited class of innovation distributions. In the text an algorithm leading to an effective solution of the problem is also proposed. The algorithm is slower than the one for the classical setup, but due to increasing computational power and stronger support of parallel computing, it can be executed in a reasonable time for models, where the number of parameters isn't very high.