Schoenberg, Ronald with Albert J. Bergersen, "Decomposing the Long Wave Through a Non-Parametric Stochastic Measurement Model", 1987
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Earlier work demonstrated the presence of two long waves of colonial administration of different lengths (1490-1825 and 1826-1969). Whether these were separate episodes or examples of deeper underlying cyclical dynamics has implications for the existence of a common system dynamic over the long wave. To further inquire into the existence of a common cyclical rhythm these larger waves were decomposed through the use of a non-parametric stochastic measurement model.To do this a 490 year time series of colonial administrations is divided into ten episodes. A conditional Normal-Poisson model is proposed based on the assumptions of a stochastic process. The mean number of colonial administrations established and terminated over each episode are estimated, controlling for a quadratic time trend which would be induced if the system was not constant throughout an episode as assumed. Two sub-cycles are observed withing each of the two long waves of colonial administrations previously reported (Bergesen and Schoenberg, 1980).The presence of these matching sub-cycles provides a strong evidence supporting a common system dynamic in not only economic but political aspects in international life.