Equivalent Number of Independent Observations: A Review

M. I. Fortus

Oboukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017 Russia

Received September 29, 1998; in final form, May 12, 1999

Abstract—For samples consisting of dependent observations, the definition most frequently used in applica-
tions for an equivalent number of independent observations N_eq is discussed. General formulas for N_eq are pre-
sented for an arbitrary finite sample and also for a sample consisting of values of a random function of a con-
tinuous argument. As an example, the calculation of N_eq corresponding to the most important statistical charac-
teristics, such as the mean, variance, and covariance, is considered. Problems concerning the application of the
formulas obtained to real series are discussed.

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