Parameter Estimation of Heavy-Tailed AR Model with Missing Data via Stochastic EM

TL;DR

This paper introduces a novel stochastic EM algorithm for estimating parameters of heavy-tailed autoregressive models with missing data, addressing a gap in handling non-Gaussian time series with incomplete observations.

Contribution

It is the first to develop a stochastic EM framework for heavy-tailed AR models with missing data, combining MCMC for efficient parameter estimation.

Findings

Algorithm converges to a stationary point of the likelihood.

Proven computational efficiency and ease of implementation.

Effective on both simulated and real-world datasets.

Abstract

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.