anticorrelated

Anticorrelated describes a relationship between two variables in which increases in one are associated with decreases in the other. It is the opposite of positive correlation. When the relationship is strong and approximately linear, the correlation coefficient is close to −1; if it is weaker or non-linear, the coefficient may still be negative, or a broader notion of anticorrelation may be used to describe inverse monotonic associations.

In statistical terms, anticorrelation is typically quantified by the Pearson correlation coefficient for linear relationships or by rank-based measures such as Spearman’s rho for monotonic associations. A negative value indicates that the variables tend to move in opposite directions. It is important to note that anticorrelation does not imply causation, and a negative association can be influenced by lurking variables, nonstationarity, or sampling bias. Nonlinear inverse relationships can exhibit anticorrelation even if the linear correlation is weak.

In time series analysis, anticorrelation can occur across observations, especially when a process exhibits mean reversion or negative autocorrelation. It can also appear in cross-correlation analysis between two series that tend to move in opposite directions with some lag.

Applications and examples vary by field. In finance, anticorrelated assets may provide diversification benefits. In physics and signal processing, anticorrelation can describe opposite responses in measurements or in noise processes with negative autocorrelation functions. Understanding anticorrelation supports data interpretation, modeling decisions, and risk assessment.

See also: correlation, negative correlation, cross-correlation, auto-correlation, causation.