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: Probably. They could be really light and small, or only use the sail to very slightly supplement the ion drive occasionally. Or just be very slow.
gollark: Maybe the sail bit could also be switchable in little bits instead of the whole thing at once, for very limited steering and communication.
gollark: Maybe space *bees* use solar sail propulsion, laser propulsion or ion engines depending on circumstance (the sail bit is switchable between reflective and photovoltaic somehow), and space *moths* use the thermal thing.
gollark: I see.
gollark: Ion drives with solar power?

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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