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Although the long-wave phenomenon has long been discussed in economic, social and political sciences, there is still highly controversial discussion about the methods of providing empirical evidence of such swings as regular cycles in economic time series. This article gives an overview about the historical development of time series methods to investigate such long-term oscillations in historical time series and to proof their regularity. It starts with a brief presentation of the methods used by Kondratieff and shows them in the context of classical business cycle analysis. It continues with ARIMA methodology and spectral analysis, which have been found to be appropriate when long waves are conceived as growth cycles. We then introduce the filter-design approach that was seen as a perfect solution to the hitherto unsolved problem of dividing trend and long waves in the low-frequency domain. A detailed discussion of the stochastic trend hypothesis and its relevance for long-wave analysis follows before outliers and trend breaks within stochastic models and their relevance for long waves are illustrated by means of the GDP per capita of the United Kingdom for 1830–2006.

A large proportion of today’s econometric literature addresses the question of whether long run GDP follows a random walk or a log linear trend with one or more structural breaks. Much less attention is paid to the modelling of the long run trend and cycle component. In most studies, the trend is simply eliminated by taking first differences of the log of the series without considering the implications of this kind of trend removal for growth and cycles. Filter design and model-based approaches are used here to assess the long run trend and the cyclical component of Chile’s per capita GDP from 1820 to 2007. Careful attention is paid to outliers and trend breaks and how they influence the appraisal of the components. We show that filter and model-based approaches give comparable results if the filter and model parameters are not chosen mechanically but tailor-made for the time series to be investigated.