In this work, we present a novel method for modeling time-varying autoregressive impulsive signals driven by symmetric alpha stable distributions. The proposed method can be interpreted as a two-stage Gibbs sampler composed of a particle filter, which is capable of estimating the unknown time-varying autoregressive coefficients, and a hybrid Monte Carlo method for estimating the unknown but constant distribution parameters of a symmetric alpha stable process. This method is an alternative to a recently published technique in which both the autoregressive coefficients and the distribution parameters are estimated jointly within a single sequential Monte Carlo framework—the single particle filter technique. The proposed method achieves lower error variances in estimating the distribution parameters compared with the single sequential Monte Carlo technique, and thus, successfully models symmetric impulsive signals.