Parameter Estimation of Heavy-Tailed AR(p) Model from Incomplete Data

The autoregressive (AR) model is a widely used model to represent the time series data from numerous applications, for example, financial time series, DNA microarray data, etc. In all such applications, issues with missing values frequently occur in the data observation or recording process. Traditionally, the parameter estimation for AR models of order p (AR(p)), from data with missing values has been considered under the Gaussian innovation assumption, and there does not exist any work addressing the issue of missing data for the heavy-tailed AR(p) model. This paper proposes an efficient framework for the parameter estimation from incomplete heavy-tailed AR(p) time series based on the stochastic approximation expectation maximization (SAEM) coupled with a Markov Chain Monte Carlo (MCMC) procedure. The proposed algorithm is computationally cheap and easy to implement. Simulation results demonstrate the efficacy of the proposed framework.