Optimization of the Generalized Covariance Estimator in Noncausal Processes

TL;DR

This paper enhances the optimization of the Generalized Covariance estimator for mixed causal and noncausal models by employing Simulated Annealing to avoid local minima, demonstrated through empirical commodity price data.

Contribution

It introduces the use of Simulated Annealing for optimizing the GCov estimator, improving identification accuracy in mixed causal/noncausal models.

Findings

SA effectively avoids local minima in GCov estimation.

Improved estimation accuracy in empirical application.

Robustness against model misspecification.

Abstract

This paper investigates the performance of the Generalized Covariance estimator (GCov) in estimating and identifying mixed causal and noncausal models. The GCov estimator is a semi-parametric method that minimizes an objective function without making any assumptions about the error distribution and is based on nonlinear autocovariances to identify the causal and noncausal orders. When the number and type of nonlinear autocovariances included in the objective function of a GCov estimator is insufficient/inadequate, or the error density is too close to the Gaussian, identification issues can arise. These issues result in local minima in the objective function, which correspond to parameter values associated with incorrect causal and noncausal orders. Then, depending on the starting point and the optimization algorithm employed, the algorithm can converge to a local minimum. The paper proposes the use of the Simulated Annealing (SA) optimization algorithm as an alternative to conventional numerical optimization methods. The results demonstrate that SA performs well when applied to mixed causal and noncausal models, successfully eliminating the effects of local minima. The proposed approach is illustrated by an empirical application involving a bivariate commodity price series.