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.
| 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).