A copula defines the probability that observations from two time series lie below given quantiles. It is proposed that stationarity tests constructed from indicator variables be used to test against the hypothesis that the copula is changing over time. Tests associated with different quantiles...

This book provides a description of the main macroeconomic models used by the European Central Bank and the euro area national central banks (Eurosystem). These models are used to help prepare economic projections and scenario analysis for individual countries and the euro area as a whole.

This paper discusses the use of preliminary data in econometric forecasting. The standard practice is to ignore the distinction between preliminary and final data, the forecasts that do so here being termed naïve forecasts. It is shown that in dynamic models a multistep-ahead naïve forecast...

This Paper considers forecasting by econometric and time series models using preliminary (or provisional) data. The standard practice is to ignore the distinction between provisional and final data. We call the forecasts that ignore such a distinction naïve forecasts, which are generated as...