Autocorrelation
Autocorrelation
Autocorrelation (pronounced: auto-correlation), also known as serial correlation, is a mathematical tool used in statistics, signal processing, and data analysis. The term is derived from the prefix 'auto-', meaning self, and 'correlation', which refers to the degree of association between two variables.
Definition
Autocorrelation is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations as a function of the time lag between them.
Mathematical Representation
The autocorrelation of a real, discrete-time signal x(n) is a function R_xx(m) that is defined as follows:
R_xx(m) = E[x(n+m)x(n)]
where E is the expected value operator, and m is the delay.
Applications
Autocorrelation is used in various fields such as economics, physics, astronomy, and biology. In econometrics, for example, autocorrelation is used to understand the reliability of regression models.
Related Terms
- Cross-correlation: A measure of similarity of two series as a function of the displacement of one relative to the other.
- Correlation coefficient: A measure that determines the degree to which two variables' movements are associated.
- Signal processing: The analysis, interpretation, and manipulation of signals.
External links
- Medical encyclopedia article on Autocorrelation
- Wikipedia's article - Autocorrelation
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