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Confidence intervals for time averages in the presence of long‐range correlations, a case study on Earth surface temperature anomalies
Author(s) -
Massah M.,
Kantz H.
Publication year - 2016
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2016gl069555
Subject(s) - uncorrelated , range (aeronautics) , hurst exponent , confidence interval , detrended fluctuation analysis , statistics , time series , gaussian , series (stratigraphy) , rescaled range , climatology , mathematics , environmental science , statistical physics , geology , physics , scaling , materials science , paleontology , geometry , quantum mechanics , composite material
Time averages, a standard tool in the analysis of environmental data, suffer severely from long‐range correlations. The sample size needed to obtain a desired small confidence interval can be dramatically larger than for uncorrelated data. We present quantitative results for short‐ and long‐range correlated Gaussian stochastic processes. Using these, we calculate confidence intervals for time averages of surface temperature measurements. Temperature time series are well known to be long‐range correlated with Hurst exponents larger than 1/2. Multidecadal time averages are routinely used in the study of climate change. Our analysis shows that uncertainties of such averages are as large as for a single year of uncorrelated data.