Effective Sample Size of the Cumulative Values of a Time Series
9 Pages Posted: 17 Oct 2016 Last revised: 8 Jul 2017
Date Written: October 16, 2016
In the computation of cumulative values of a time series of length N, all data items except for the last item are used more than once. The multiplicity in the use of the data reduces the effective value of N. We show that for time series of cumulative values the effective value of N is too small to yield sufficient degrees of freedom to make inferences about the population. It is not possible to evaluate the statistical significance of a correlation between cumulative values for this reason even when the magnitude of the correlation coefficient observed in the sample is large. The results provide a rationale for the findings of a previous work in which the spuriousness of correlations between cumulative values was demonstrated with Monte Carlo simulation.
Keywords: IPCC, fossil fuel emissions, global warming, climate change, AGW, cumulative emissions, cumulative warming, correlation coefficient, spuriousness of correlations between cumulative values, hypothesis test for correlation, degrees of freedom, multiplicity of data use, effective value of n
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