Modelling the Trend: The Historical Origins of Some Modern Methods and Ideas

Abstract

Abstract. The development of the methods of correlation and regression analysis at the turn of the 20th century led to their use in attempting to identify relationships between economic variables. However, caution was soon expressed that correlating series with 'secular' trends was likely to be misleading. After some discussion of methods, linear detrending by least-squares estimation became the default method. By the 1920s, however, some voices of dissent expressed the view that linear detrending was likely to be inappropriate in some, even many, cases. This led to a number of innovative methodological developments, including rolling window estimation, moving integration, non-linear trends, structural breaks, sigmoid-type smooth adjustment functions, the beginnings of stochastic trend modelling and the construction of 'smoothers' and filters. Although generally failing to have an impact at the time, all substantially predate their current use in econometrics. This paper establishes precedence for these ideas and recreates some of the empirical examples and early simulations. Keywords