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...

This paper examines whether the interest rate preferences of Federal Reserve Bank Presidents are subject to a regional bias. In order to evaluate the regional bias hypothesis, we augment individual Taylor rules for the Federal Reserve Bank Presidents (sample 1989 to 2006) with regional variables...

This paper examines whether the interest rate preferences of Federal Reserve Bank Presidents are subject to a regional bias. In order to evaluate the regional bias hypothesis, we augment individual Taylor rules for the Federal Reserve Bank Presidents (sample 1989 to 2006) with regional variables...

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 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...

In this paper, we propose a framework to evaluate the subjective density forecasts of macroeconomists using micro data from the euro area Survey of Professional Forecasters (SPF). A key aspect of our analysis is the evaluation of the entire predictive densities, including an evaluation of the...

We propose methods to evaluate the risk assessments collected as part of the ECB Survey of Professional Forecasters (SPF). Our approach focuses on direction-of-change predictions as well as the prediction of relatively more extreme macroeconomic outcomes located in the upper and lower regions of...