Optimization of the generalized covariance estimator in noncausal processes

Gianluca Cubadda, Francesco Giancaterini*, Alain Hecq, Joann Jasiak

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


This paper investigates the performance of routinely used optimization algorithms in application to the Generalized Covariance estimator (GCov) for univariate and multivariate mixed causal and noncausal models. The GCov is a semi-parametric estimator with an objective function based on nonlinear autocovariances to identify causal and noncausal orders. When the number and type of nonlinear autocovariances included in the objective function are 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 Simulated Annealing (SA) optimization algorithm as an alternative to conventional numerical optimization methods. The results demonstrate that SA performs well in its application to mixed causal and noncausal models, successfully eliminating the effects of local minima. The proposed approach is illustrated by an empirical study of a bivariate series of commodity prices.
Original languageEnglish
Article number127
Number of pages20
JournalStatistics and Computing
Issue number4
Publication statusPublished - 1 Aug 2024


  • Mixed causal and noncausal models
  • Generalized covariance estimator
  • Simulated Annealing
  • Optimization
  • Commodity prices


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