Regularized Generalized Covariance (RGCov) Estimator

This paper proposes the Regularized Generalized Covariance (RGCov) estimator, a ridge-type extension of the Generalized Covariance (GCov) estimator for high-dimensional stationary time series. By regularizing the GCov objective function, which involves the inverse of the covariance matrix, RGCov improves numerical stability while preserving positive definiteness. Under suitable conditions, the new estimator is consistent, asymptotically normal, and semiparametrically efficient. We also extend the GCov specification test and the nonlinear serial dependence (NLSD) test to their regularized versions, both of which are asymptotically Chi-square distributed. Simulation studies confirm the reliability of the RGCov and associated tests in high-dimensional settings. In the empirical application, RGCov is used to estimate a mixed causal-noncausal VAR for green energy stocks in the Renixx index and to construct two bubble-based investment strategies: bubble-riding and bubble-hedging, both of which outperform the benchmark index.