Robust Maximum Likelihood Estimation of Sparse Vector Error Correction Model

TL;DR

This paper introduces a robust estimation method for vector error correction models that handles heavy-tailed data and outliers by using a Cauchy distribution, incorporating sparsity for feature selection, and employing an efficient MM algorithm.

Contribution

It proposes a novel robust estimation approach for VECMs using Cauchy distribution and sparsity, solved via an efficient MM algorithm, addressing limitations of traditional Gaussian-based methods.

Findings

The proposed method effectively handles heavy-tailed data and outliers.

Numerical simulations demonstrate the algorithm's efficiency and robustness.

Sparsity enables feature selection and dimension reduction in VECM estimation.

Abstract

In econometrics and finance, the vector error correction model (VECM) is an important time series model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heavy-tailed data and outliers can lead to the inapplicability of these methods. In this paper, we propose a robust model estimation method based on the Cauchy distribution to tackle this issue. In addition, sparse cointegration relations are considered to realize feature selection and dimension reduction. An efficient algorithm based on the majorization-minimization (MM) method is applied to solve the proposed nonconvex problem. The performance of this algorithm is shown through numerical simulations.