The rank of the Hankel matrix, corresponding to a system transfer function, is equal to the order of its minimal state space realization. The computation of the rank of the Hankel matrix is complicated by the fact that its block elements are rarely given exactly but are estimated instead. In...

The rank of the spectral density matrix conveys relevant information in a variety of modelling scenarios. Phillips (1986) showed that a necessary condition for cointegration is that the spectral density matrix of the innovation sequence at frequency zero is of a reduced rank. In a recent paper...

The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive de?nite matrix estimate...

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics...

Testing and estimating the rank of a matrix of estimated parameters is key in a large variety of econometric modelling scenarios. This paper describes general methods to test for and estimate the rank of a matrix, and provides details on a variety of modelling scenarios in the econometrics...

We propose a theoretical framework for assessing whether a forecast model estimated over one period can provide good forecasts over a subsequent period. We formalize this idea by defining a forecast breakdown as a situation in which the out-of-sample performance of the model, judged by some loss...

We propose a theoretical framework for assessing whether a forecast model estimated over one period can provide good forecasts over a subsequent period. We formalize this idea by defining a forecast breakdown as a situation in which the out-of-sample performance of the model, judged by some loss...