  The autoregressive (AR) model is a widely used model to understand time
series data. Traditionally, the innovation noise of the AR is modeled as
Gaussian. However, many time series applications, for example, financial time
series data, are non-Gaussian, therefore, the AR model with more general
heavy-tailed innovations is preferred. Another issue that frequently occurs in
time series is missing values, due to system data record failure or unexpected
data loss. Although there are numerous works about Gaussian AR time series with
missing values, as far as we know, there does not exist any work addressing the
issue of missing data for the heavy-tailed AR model. In this paper, we consider
this issue for the first time, and propose an efficient framework for parameter
estimation from incomplete heavy-tailed time series based on a stochastic
approximation expectation maximization (SAEM) coupled with a Markov Chain Monte
Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and
easy to implement. The convergence of the proposed algorithm to a stationary
point of the observed data likelihood is rigorously proved. Extensive
simulations and real datasets analyses demonstrate the efficacy of the proposed
framework.
