Karhunen-Loève Analysis of Historical Time Series With an Application to Plantation Births in Jamaica

A comparison of two spectral analysis procedures is presented: the frequency domain (Fourier transform) model and the Karhunen-Loeve time domain model. Both models are used in turn to analyze a plantation births series during the period 1880-1938. The principal components model can be adapted as the discrete analogue of the Karhunen-Loeve stochastic integral equation in order to decompose a single time series into trend, cycle, and seasonality. The results indicate that the Karhunen-Loeve decomposition, which has been less popular in applied work than the frequency domain model, can provide the social historian with useful results that are easier to interpret.