Introduction to Einstein's Contribution to Time-series Analysis
William A. Cardner · 1987
HE HISTORY of ideas evolves endlessly, sometimes becoming more accurate with the passage of time, sometimes more distorted. This is so even for ideas originating as recently as 100 years ago. In spite of the documentation provided by published books and papers, personal letters, and recollections, historians are inevitably limited by the substantial loss of information with the passing of participants and by the unavoidable subjectivityof the historians’ own interpretations of the available information. The recent discovery of a long forgotten early paper by Albert Einstein on the topic of time-series analysis [I] provides an interesting example of the evolutionary process of tracing the history of ideas. This very brief paper, entitled ”Method for the determination of the statistical values of observations concerning quantities subject to irregular fluctuations,’’ was originally published in the Archives des Sciences Physiques et Naturelles in 1914 following an oral presentation at a meeting of the Swiss Physical Society earlier that year. An English translation of this paper is reproduced in this issue of the ASSP Magazine. The paper discusses the autocorrelation function and its relationship to the spectral content of a time-series, the crosscorrelation function as a measure of interdependence of two time-series, and two methods for measurementor computation of spectral content: the frequency-smoothed periodogram method and the Fourier-transformed autocorrelation method. Two experts in the field of time-series analysis, Professor A. M. Yaglom from the Instituteof Atmospheric Physics, Academy of Sciences of the USSR, and Professor P. R. Masani from the Department of Mathematics, University of Pittsburgh, have written extensive commentaries on this paper and its place in the history of time-series analysis [2], [3]. The differences in the backgrounds and points of view of this physicist and this mathematician have led to some interesting differences in their interpretations of Einstein‘s accomplishments in his paper.