Life-time of correlation

In probability theory and related fields, the life-time of correlation measures the timespan over which there is appreciable autocorrelation or cross-correlation in stochastic processes.

Definition

Correlation	Negative	Positive
Weak	−0.5 to 0.0	0.0 to 0.5
Strong	−1.0 to −0.5	0.5 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).