A RAPID METHOD FOR ASCERTAINING SERIAL LAG CORRELATION

Abstract

The search for a mechanical means for rapidly assessing the similarity between two time series, and particularly for matching series of tree ring width measurements, has led the writer to construct a photoelectric device for the comparison of time series in the form of bar graphs. This paper is a discussion of a method and some problems of serial lag correlation by photoelectric measurement of such bar graphs. Portions of the theory developed in this connexion are also relevant to the rapid calculation of serial lag correlation by ordinary means. The study of tree ring width series, called dendrochronology, had its inception chiefly in the researches of the astronomer and climatologist, A. E. Douglass (1919, 1928, 1936). This study makes use of the fact that trees of the same species growing under similar conditions within a given climatic region agree to a considerable extent in the variations in width of their annual growth rings. By matching or 'cross-identifying-' overlapping series of ring widths, extending back from living trees to ancient specimens collected from prehistoric sites in the south-western United States, Douglass and his colleagues have established the average tree ring width record for nearly 2000 years past. This record gives valuable information concerning the climatic fluctuations of the period. By matching the rings of timbers from archaeological sites with the master ring width record at the proper position, the approximate year of construction for a great number of prehistoric habitations in this region has been determined. The problem of cross-identifying two tree ring width series is the problem of determining the relative position in which they are most similar, and in which the similarity is, with high probability, due to the same climatic factors rather than either to mere chance or to harmonic features displaced by an integral number of cycles. This problem is analogous to that of discovering the lag between two time series in economic, physical, and other studies. In the latter type of serial correlation problem the time bases are known for each series, i.e. each measurement corresponds to a known point on the time scale, but the lag remains to be discovered. Such problems might be termed dyschronous. In the dendrochronological problem the time base of one series is unknown, but the lag is known to be zero. By matching the two series, the time base of the unknown series may be determined from the known series. Such problems might be termed synchronous. The match position in synchronous serial correlation corresponds to the lag position in dyschronous correlation. The standard statistical correlation procedures are much too time-consuming for use in cross-identification where large numbers of tree ring series must be compared at innumerable match hypotheses. The photoelectric method of comparing bar graphs of time series is designed specifically for the rapid computation of measures of similarity between such series. It is equally applicable to dyschronous serial correlation, and to autocorrelation by employing pairs of identical graphs.