In the literature, impulsive signals are mostly modeled by symmetric alpha-stable processes. To represent their temporal dependencies, usually autoregressive models with time-invariant coefficients are utilized. We propose a general sequential Bayesian modeling methodology where both unknown autoregressive coefficients and distribution parameters can be estimated successfully, even when they are time-varying. In contrast to most work in the literature on signal processing with alpha-stable distributions, our work is general and models also skewed alpha-stable processes. Successful performance of our method is demonstrated by computer simulations. We support our empirical results by providing posterior Cramer–Rao lower bounds. The proposed method is also tested on a practical application where seismic data events are modeled.