Stochastic and deterministic trend models

Abstract

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.