Modelling the long wave-phenomena

Abstract

Der vorliegende Beitrag diskutiert einige statistische und mathematische Probleme der 'langen Wellen', d.h. dem Phänomen regelmäßiger, sich in langen Zeiträumen wiederholender Abläufe. Gezeigt wird, wie Informationen über 'lange Wellen' aus Zeitreihen und einem Filter-Design abgeleitet werden können. Dieser Ansatz steht im engen Zusammenhang mit der Methodologie der Zeitreihenanalyse. Das vorgestellte parametrische Modell beansprucht prognostische Relevanz (zumindest für die im Text benutzten Daten). (pmb)

'In this paper, by 'modelling' we mean the identification and estimation of time series models and not the development and evaluation of economic-theoretical models. Whereas the latter mentioned approach aims at analysing the probable causes of wave-phenomena, the time-series approach is a purely empirical one. If it should prove to be possible to identify timeseries models, we can hope that they will possess predictive power and we can further hope that this will help us in finding dependencies between different wave-series. This would make it possible to conduct multivariate analyses of wave-phenomena which have to the best of our knowledge not been performed yet. However, in this paper we restrict ourselves to univariate modelling for two reasons: in the first place, we think that sufficient experience must be accumulated in univariate modelling before multivariate modelling can be done properly, and secondly, even univariate modelling of long wave-phenomena by means of modern time series analysis is a topic not discussed up to now (as far as we know).' (author's abstract)