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Parameter Estimation of Heavy-Tailed Random Walk Model from Incomplete Data

This paper proposes a novel and structured framework for parameter estimation from incomplete time series data under heavy-tailed random walk model. Traditionally, maximum likelihood estimation (MLE) for Gaussian random walk model from incomplete data has been considered. However, it is not applicable in many practical applications that follow some heavy-tailed random walk model. We first model a random walk model with Student-t residuals. Then we develop an MLE-based stochastic expectation maximization (EM) algorithm. The algorithm provides tractable E and M steps, which are easy to implement with simple updates and fast convergence. The simulation results illustrate the improved performance over the benchmarks.