We develop a new version of the production function (PF) approach usually used for estimating the output gap of the euro area. Our version does not call for any (often imprecise) measure of the capital stock and improves the estimation of the trend total factor productivity. We asses this...

A univariate first order stochastic cycle can be represented as an element of a bivariate first order vector autoregressive process, or VAR(1), where the transition matrix is associated with a Givens rotation. From the geometrical viewpoint, the kernel of the cyclical dynamics is described by a...

The paper focuses on the comparison of the direct and iterated AR predictors for difference stationary processes. In particular, it provides new methods for comparing the efficiency of the two predictors and for extracting the trend from macroeconomic time series using the two methods. 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...

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...

Seasonality is one of the most important features of economic time series. The possibility to abstract from seasonality for the assessment of economic conditions is a widely debated issue. In this paper we propose a strategy for assessing the role of seasonal adjustment on business cycle...

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...

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...

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...

The variance profile is defined as the power mean of the spectral density function of a stationary stochastic process. It is a continuous and non-decreasing function of the power parameter, p, which returns the minimum of the spectrum (p → −∞), the interpolation error variance (harmonic...