A New Bispectral Test for Nonlinear Serial Dependence

Bispectrum, nonlinearity, time series analysis

Stochastic and deterministic trend models

In this paper we provide an overview of some trend models formulated for global and local estimation. Global trend models are based on the assumption that the trend or nonstationary mean of a time series can be approximated closely by simple functions of time over the entire span of the series. The most common representation of deterministic and stochastic trend are introduced. In particular, for the former we analyze polynomial and transcendental functions, whereas for the latter we assume that the series from which the trend will be identified follows a homogeneous linear nonstationary stochastic process. Recently more attention has been oriented on the analysis of the short term trend, that includes cyclical fluctuations and is referred to as trend-cycle. At this regard, we analyze the local polynomial regression predictors developed by Henderson (1916) and LOESS due to Cleveland (1979), which are the most widely applied to estimate the short term local trend of seasonally adjusted economic indicators

Business Cycles and Current Economic Analysis

This is a brief introduction to the special issue on �New Developments in Modelling and Estimation of Economic Cycles� . The concept and definition of economic and business cycles are discussed together with two main schools of thought, the Keynesian and the neoclassical. Until the Keynesian revolution in mainstream economics in the wake of the Great Depression, classical and neoclassical explanations were the mainstream explanation of economic cycles; following the Keynesian revolution, neoclassical macroeconomics was largely rejected. There has been some resurgence of neoclassical approaches in the form of real business cycle (RBC) theory. Real business cycle theory is a class of macroeconomic model in which business cycle fluctuations to a large extent can be accounted for by real (in contrast to nominal) shocks. In a broad sense , there have been two ways by which economic and business cycles have been studied, one analyzing complete cycles and the other, studying the behavior of the economic indicators during incomplete phases by comparing current contractions or expansions whith corresponding phases in the past in order to assess current economic conditions. Two different methodologies have been applied for current economic analysis, the parametric one, that makes use of filters based on models, such as ARIMA and State Space models , and the other based on nonparametric digital filtering. Some of the invited papers of this issue deal with this second approach.Esta es una breve introducción a la edición especial titulada �Nuevos Desarrollos en Modelización y Estimación de Ciclos Económicos� donde se discuten los conceptos y definiciones del ciclo económico conjuntamente con el pensamiento de dos escuelas, la keynesiana y la neoclásica. Antes de la revolución keynesiana al comienzo de la Gran depresión, las explicaciones clásicas y neoclásicas del ciclo económico fueron las dominantes; después de la revolución keynesiana, la macroeconomía neoclásica fue ampliamente rechazada. Existe hoy un resurgimiento del enfoque neoclásico bajo la forma del ciclo económico real (CER). En la teoría el ciclo económico real las fluctuaciones del ciclo pueden ser explicadas preponderantemente por medio de shocks reales en contraste a shocks nominales. En un sentido amplio, dos enfoques han sido utilizados para el estudio de los ciclos económico y de los negocios; uno de ellos analiza ciclos completos y el otro, estudia el comportamiento de indicadores económicos durante fases incompletas mediante la comparación de contracciones o expansiones actuales con las mismas fases en periodos anteriores, a fin de evaluar el estado de las condiciones económicas actuales. Hay dos métodos para modelizar las condiciones económicas actuales, una paramétrica, que usa filtros resultantes de modelos tales como los ARIMA o los modelos State space, y un segundo procedimiento que se basa en filtros digitales no paramétricos. Algunos de los artículos invitados en esta publicación se ocupan de este segundo enfoqu