Generalized Covariance Estimator

TL;DR

This paper introduces the Generalized Covariance (GCov) estimator for a broad class of semi-parametric dynamic models, demonstrating its efficiency and applicability to models including VAR, structural VAR, and nonlinear models like ARCH-M.

Contribution

The paper proposes the GCov estimator, a novel residual-based method that is semi-parametrically efficient and applicable to various complex dynamic models, with proven asymptotic properties.

Findings

GCov estimator is semi-parametrically efficient.

Residual-based portmanteau statistic is asymptotically chi-square.

Finite sample performance is validated through simulations.

Abstract

We consider a class of semi-parametric dynamic models with strong white noise errors. This class of processes includes the standard Vector Autoregressive (VAR) model, the nonfundamental structural VAR, the mixed causal-noncausal models, as well as nonlinear dynamic models such as the (multivariate) ARCH-M model. For estimation of processes in this class, we propose the Generalized Covariance (GCov) estimator, which is obtained by minimizing a residual-based multivariate portmanteau statistic as an alternative to the Generalized Method of Moments. We derive the asymptotic properties of the GCov estimator and of the associated residual-based portmanteau statistic. Moreover, we show that the GCov estimators are semi-parametrically efficient and the residual-based portmanteau statistics are asymptotically chi-square distributed. The finite sample performance of the GCov estimator is illustrated in a simulation study. The estimator is also applied to a dynamic model of cryptocurrency prices.