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Summary 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…

平稳向量自回归模型中的长期风险AI 解读

This paper introduces a local-to-unity/small sigma model for stationary processes with long-range persistence and non-negligible long-run prediction and estimation risks. The model represents a process containing unobserved short and long-run components measured on different time scales. The short-run component is defined in calendar time, while the long-run component evolves in rescaled time with ultra-long units. We develop estimation and long-run prediction methods for…

广义协方差估计量AI 解读

We consider a class of semi-parametric dynamic models with iid errors, including the nonlinear mixed causal-noncausal Vector Autoregressive (VAR), Double-Autoregressive (DAR) and stochastic volatility models. To estimate the parameters characterizing the (nonlinear) serial dependence, we introduce a generic Generalized Covariance (GCov) estimator, which minimizes a residual-based multivariate portmanteau statistic. In comparison to the standard methods of moments, the GCov…

自回归过程中的非因果阶数误设AI 解读

This paper examines noncausal order misspecification in noncausal and mixed processes. We consider the constrained maximum likelihood (ML) estimators of autoregressive parameters obtained when noncausal order s is fixed and potentially different from the true order s0. The effect of such noncausal order misspecification on the constrained ML estimators of the autoregressive parameters is examined by means of the binding function. We find that, surprisingly, the misspecified…

非因果向量自回归过程：表示、识别与半参数估计AI 解读

This paper introduces a representation theorem for a mixed VAR(p) process by distinguishing its causal and noncausal components. That representation is used to discuss the advantages and limitations of second-order identification in a mixed VAR. We show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function, while nonlinear autocovariances are needed to distinguish between them. The paper…

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