The expectation-maximization algorithm for autoregressive models with normal inverse Gaussian innovations

TL;DR

This paper introduces an EM algorithm for estimating parameters of autoregressive models with NIG innovations, effectively modeling data with outliers and jumps, and demonstrates its advantages over classical methods on simulated and real financial data.

Contribution

It develops a novel EM-based estimation method for AR models with NIG innovations, addressing limitations of classical Gaussian-based models.

Findings

EM algorithm accurately estimates model parameters

NIG-based AR models better capture data jumps and outliers

Method outperforms Yule-Walker and least squares in simulations and real data

Abstract

The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal distribution. However, this distribution does not allow describing data with outliers and asymmetric behavior. In this paper, we study the AR models with normal inverse Gaussian (NIG) innovations. The NIG distribution belongs to the class of semi heavy-tailed distributions with wide range of shapes and thus allows for describing real-life data with possible jumps. The expectation-maximization (EM) algorithm is used to estimate the parameters of the considered model. The efficacy of the estimation procedure is shown on the simulated data. A comparative study is presented, where the classical estimation algorithms are also incorporated, namely, Yule-Walker and conditional least squares methods along with EM method for model parameters estimation. The applications of the introduced model are demonstrated on the real-life financial data.