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Explore the mathematical foundations and practical implications of Yule's nonsense correlation phenomenon in this 48-minute conference talk. Delve into the 1926 discovery by statistician G. Udny Yule showing that empirical correlation coefficients between two independent standard random walks do not converge to zero but instead converge in distribution to a diffuse law across the entire interval (-1,1). Examine how this contrasts sharply with classical results for independent and identically distributed data sequences, where correlation converges to zero. Learn about the serious misapplications of this statistical concept in environmental observational studies and climate science attribution research. Understand the mathematical framework underlying Yule's nonsense correlation through Donsker's theorem, where Pearson correlation of two random walks converges to a ratio of quadratic functionals of Wiener processes. Discover new research on fluctuations around this convergence, including findings that n(ρ − ρn) has an asymptotic distribution in the second Wiener chaos with characteristics both exogenous and conditional on the original data. Analyze the implications for practical independence testing and environmental time series attribution, including conjectures about the exotic 1/n fluctuation scale rather than the typical 1/n^(1/2) scale in standard central limit theorems.
