A Suggestion for the Presentation of Correlations and Their Significance Levels

Abstract

It is suggested that the results of correlation calculations between concurrent time series be presented in the form of normalized correlations, the normalization factor being the estimated large-lag standard error. This factor is easily estimated from the data using the Bartlett formula and reflects the interplay of the dominant time scales of the input processes and the finite record length. It is shown that significance levels are inherent in the normalized correlations and the procedure used to obtain them is mathematically equivalent to that now widely used in oceanography. Abstract It is suggested that the results of correlation calculations between concurrent time series be presented in the form of normalized correlations, the normalization factor being the estimated large-lag standard error. This factor is easily estimated from the data using the Bartlett formula and reflects the interplay of the dominant time scales of the input processes and the finite record length. It is shown that significance levels are inherent in the normalized correlations and the procedure used to obtain them is mathematically equivalent to that now widely used in oceanography.