ABSTRACT
The estimation of the nonstationary mean of a seasonally adjusted time series, defined as trend-cycle, has attracted the attention of many statisticians and actuaries for a long time. Two major approaches have been followed, one parametric, or model-based, and the other nonparametric, or based on linear digital filtering. The most common assumption in the parametric approach is that the nonstationary mean can be represented by a stochastic model belonging to the ARIMA Box and Jenkins (1976) class or a random walk with or without a random drift. Major significant contributions have been made by Akaike (1980), Gersch and Kitagawa (1983), Harvey and Jaeger (1993), King and Rebelo (1993), Go´mez and Maravall (1994), Maravall (1993), Harvey (1997), Go´mez (1999), and Kaiser and Maravall (1999) among others.
