Statistical Validation of The Unified Cycle Theory. Purposes: Objectively determine wavelengths for the Extra-Universal Wave Series cycles. Test the null hypothesis that random fluctuations cause the EUWS cycles. If a question refers to a specific graph, please note the slide number →.
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Objectively determine wavelengths for the Extra-Universal Wave Series cycles.
Test the null hypothesis that random fluctuations cause the EUWS cycles.
If a question refers to a specific graph, please note the slide number →
Lomb-Scargle Periodogram – Spectral analysis method for determining the power of cycles detected in a time-series.
Smoothed Periodogram – Estimates a wavelength when several peaks cluster together. Also used for determining confidence levels.
Lagged Correlation Analysis – Used to compare time-series data to a model for all lags. This type of analysis assesses when the various EUWS cycles actually peaked and troughed.
Monte Carlo Simulation – Random sequences generated to test their correlation to the model used in the Lagged Correlation Analysis.
Probability Mass Function – Used for testing significance when only one phase of a cycle is certain, while other phases are unknown or less certain.
Criteria A – For a time-series with minimal gaps in the data:
Note for Cycles below 1-Myr: For higher frequency cycles, delays following EUWS strikes often occur in global climate proxies because of natural response lags . In these cases, the lead-lag analysis becomes meaningless as a validation tool.
Criteria B – Used when one phase of a cycle is better known than other phases:
Because of time limitations, this review of EUWS tests must stop at 516-yr. This completes the statistical evaluation.
The hypothesis that random fluctuations cause the EUWS cycles has been rejected consistently for all but two of the cycles between 9.57-day and 822-gyr. To continue using a hypothesis of randomness, a proponent of choas must explain why a subjective judgment of randomness is preferred over the statistical assessment of EUWS periodicity.