The paper concerns the design of nonparametric low-pass filters that have the property of reproducing a polynomial of a given degree. Two approaches are considered. The first is locally weighted polynomial regression (LWPR), which leads to linear filters depending on three parameters: the...

The chapter deals with parametric models for the measurement of the business cycle in economic time series. It presents univariate methods based on parametric trend{cycle decom- positions and multivariate models featuring a Phillips type relationship between the output gap and inflation and the...

This paper examines the comovements of construction in Italy's regions from 1861 to 1913. The dynamic correlations of the series' deviation cycles decline in the case of buildings, remain very low in that of railways, and tend to decline in that of other infrastructure; the total-construction...

The paper focuses on the comparison of the direct and iterated AR predictors when Xt is a difference stationary process. In particular, it provides some useful results for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two...

We address the problem of seasonal adjustment of a nonlinear transformation of the original time series, such as the Box-Cox transformation of a time series measured on a ratio scale, or the Aranda-Ordaz transformation of proportions, which aims at enforcing two essential features: additivity...

The paper estimates a large-scale mixed-frequency dynamic factor model for the euro area, using monthly series along with Gross Domestic Product (GDP) and its main components, obtained from the quarterly national accounts. The latter define broad measures of real economic activity (such as GDP...

This note is concerned with the spectral properties of matrices associated with linear smoothers. We derive analytical results on the eigenvalues and eigenvectors of smoothing matrices by interpreting the latter as perturbations of matrices belonging to algebras with known spectral properties,...

We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and...

Trend estimation deals with the characterization of the underlying, or long–run, evolution of a time series. Despite being a very pervasive theme in time series analysis since its inception, it still raises a lot of controversies. The difficulties, or better, the challenges, lie in the...

The Beveridge-Nelson decomposition defines the trend component in terms of the eventual forecast function, as the value the series would take if it were on its long-run path. The paper introduces the multistep Beveridge-Nelson decomposition, which arises when the forecast function is obtained by...