Do Kondratieff waves exist? How time series techniques can help to solve the problem.

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.