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Understanding Red Noise in Climate Data: Degrees of Freedom and Significance Testing Dangers

This study explores the implications of red noise in climate datasets, focusing on the effective degrees of freedom (DOFs) and the dangers of statistical significance tests. It highlights how assumptions about autocorrelation and time series length can lead to misleading conclusions. Using sunspot data as a case study, we demonstrate the risks of spurious correlations arising from mixed frequency datasets. The findings underscore the need for a cautious interpretation of statistical relationships in climate science, as low-frequency signals can distort our understanding of longer-term trends.

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Understanding Red Noise in Climate Data: Degrees of Freedom and Significance Testing Dangers

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  1. Red noise time series illustratingdegrees of freedom (DOFs) and some significance test dangerscommon to climate Brian Mapes MPO 542 Spring 2014

  2. Sunspots and hurricanes • http://onlinelibrary.wiley.com/doi/10.1029/2008GL034431/pdf

  3. Dangerous datasets: two freqs low pass filter of sunspots

  4. Statistical tests assume red noise

  5. "Effective degrees of freedom":time series length/ autocor decay time • lag at which correlation decays to 1/e • or maybe twice that (typical excursion duration)? • seems to work better for 1x decay time 25 months 1200/25 = 40

  6. Random fluctuations in 100y variances relative to the true (var=1) process

  7. Random correlations of 100y series ~50 DOFs implied

  8. Danger: Low + high freq mixtures data = (0.6*AR1 + 0.4*LFAR1) *sqrt(2); % Weighted sum, var=1

  9. LF + HF mixture in spectrum... HF part LF part

  10. Long tailed autocorrelation: so the e-folding time isn't the whole story! 1200/10 ~ 120 DOFs? DANGER

  11. Spurious correlations are 10x more likely than you would expect from 120 DOFs!

  12. Spurious covariance is usually in the low frequencies (long periods), which have just a few DOFs (& are prone to coincidences) While high frequencies contribute the large number of (apparent! by standard formula) effective degrees of freedom

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