Beware of correlations: When correlating two signals which both evolve slowly over time, the chances of finding a significant correlation between the two are much higher than when comparing signals which lack this property

Meijer, Guido. 2021. “Neurons in the Mouse Brain Correlate with Cryptocurrency Price: A Cautionary Tale.” PsyArXiv. April 27. doi:10.31234/osf.io/fa4wz

Abstract: In this paper I report the discovery of neurons which showed a neural correlate with ongoing fluctuations of Bitcoin and Ethereum prices at the time of the recording. I used the publicly available dataset of Neuropixel recordings by the Allen Institute to correlate the firing rate of single neurons with cryptocurrency price. Out of ~40.000 recorded single neurons, ~70% showed a significant correlation with Bitcoin or Ethereum prices. Even when using the conservative Bonferroni correction for multiple comparisons, ~35% of neurons showed a significant correlation, which is well above the expected false positive rate of 5%. These results were due to "nonsense correlations": when correlating two signals which both evolve slowly over time, the chances of finding a significant correlation between the two are much higher than when comparing signals which lack this property.