Life-time of correlation

The life-time of correlation measures the timespan over which there is appreciable autocorrelation or cross correlation in stochastic processes.

Definition
CorrelationNegativePositive
Weak−0.5 to 0.00.0 to 0.5
Strong−1.0 to −0.50.5 to 1.0

The correlation coefficient ρ, expressed as an autocorrelation function or cross-correlation function, depends on the lag-time between the times being considered. Typically such functions, ρ(t), decay to zero with increasing lag-time, but they can assume values across all levels of correlations: strong and weak, and positive and negative as in the table.

The life-time of a correlation is defined as the length of time when the correlation coefficient is at the strong level.[1] The durability of correlation is determined by signal (the strong level of correlation is separated from weak and negative levels). The mean life-time of correlation could measure how the durability of correlation depends on the window width size (the window is the length of time series used to calculate correlation).

gollark: You do realise you can upload screenshots directly into Discord?
gollark: ⅓, but yes.
gollark: 1³/3 isn't 1.
gollark: * + c
gollark: The integral of x² is x³/3, yes.

References
  1. Buda, Andrzej; Jarynowski, Andrzej (2010) Life-time of correlations and its applications vol.1, p.9, [Głogów] : Wydawnictwo Niezależne


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