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...

This paper assesses the statistical reliability of different measures of the output gap for the Euro-11 area and the US using output, inflation and unemployment systems. In order to assess the reliability of an output gap estimate two criteria are adopted. Firstly, the estimate should have...

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 main focus of this paper is to model the daily series of banknotes in circulation in the context of the liquidity management of the Eurosystem. The series of banknotes in circulation displays very marked seasonal patterns. To the best of our knowledge the empirical performance of two...

Under the Maastricht Treaty and the Stability and Growth Pact (SGP) European Union (EU) Member States commit themselves to avoid excessive deficits over 3% of GDP and to pursue the medium-term objective of budgetary positions close to balance or in surplus. The SGP provides also regulation for...

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...

This paper explains to what extent excess reserves are and should be relevant today in the implementation of monetary policy, focusing on the speci?c case of the operational framework of the Eurosystem. In particular, this paper studies the impact that changes to the operational framework for...

Standard measures of prices are often contaminated by transitory shocks. This has prompted economists to suggest the use of measures of underlying in?ation to formulate monetary policy and assist in forecasting observed in?ation. Recent work has concentrated on modelling large datasets using...

The quantity theory of money predicts a positive relationship between monetary growth and inflation over long-run horizons. However, in the short-run, transitory shocks to either money or inflation can obscure the inflationary signal stemming from money. The spectral analysis of time series...