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This paper introduces a nonlinear shrinkage estimator of the covariance matrix that does not require recovering the population eigenvalues first. We estimate the sample spectral density and its Hilbert transform directly by smoothing the sample eigenvalues with a variable-bandwidth kernel....
Persistent link: https://www.econbiz.de/10011784298
This paper constructs a new estimator for large covariance matrices by drawing a bridge between the classic Stein (1975) estimator in finite samples and recent progress under large-dimensional asymptotics. Our formula is quadratic: it has two shrinkage targets weighted by quadratic functions of...
Persistent link: https://www.econbiz.de/10012140662
Under rotation-equivariant decision theory, sample covariance matrix eigenvalues can be optimally shrunk by recombining sample eigenvectors with a (potentially nonlinear) function of the unobservable population covariance matrix. The optimal shape of this function reflects the loss/risk that is...
Persistent link: https://www.econbiz.de/10012166459
Many econometric and data-science applications require a reliable estimate of the covariance matrix, such as Markowitz portfolio selection. When the number of variables is of the same magnitude as the number of observations, this constitutes a difficult estimation problem; the sample covariance...
Persistent link: https://www.econbiz.de/10012166460
Modeling and forecasting dynamic (or time-varying) covariance matrices has many important applications in finance, such as Markowitz portfolio selection. A popular tool to this end are multivariate GARCH models. Historically, such models did not perform well in large dimensions due to the...
Persistent link: https://www.econbiz.de/10012253774
This paper constructs a new estimator for large covariance matrices by drawing a bridge between the classic Stein (1975) estimator in finite samples and recent progress under large-dimensional asymptotics. The estimator keeps the eigenvectors of the sample covariance matrix and applies shrinkage...
Persistent link: https://www.econbiz.de/10012420686
Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how...
Persistent link: https://www.econbiz.de/10013164130
Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how...
Persistent link: https://www.econbiz.de/10012588495
Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many successful proposals to address the first estimation problem exist by now. This paper addresses the second estimation problem. We promote a nonlinear...
Persistent link: https://www.econbiz.de/10011099190
This paper introduces a new method for deriving covariance matrix estimators that are decision-theoretically optimal. The key is to employ large-dimensional asymptotics: the matrix dimension and the sample size go to infinity together, with their ratio converging to a finite, nonzero limit. As...
Persistent link: https://www.econbiz.de/10011082366