Editing Autocorrelation (section)

{{Short description|Correlation of a signal with a time-shifted copy of itself, as a function of shift}}
{{Correlation and covariance}}
[[File:Acf new.svg|thumb|300px|right|Above: A plot of a series of 100 random numbers concealing a [[sine]] function. Below: The sine function revealed in a [[correlogram]] produced by autocorrelation.]]
[[File:Comparison convolution correlation.svg|thumb|400px|Visual comparison of convolution, [[cross-correlation]], and '''autocorrelation'''.  For the operations involving function {{mvar|f}}, and assuming the height of {{mvar|f}} is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point.  Also, the symmetry of {{mvar|f}} is the reason <math>g*f</math> and <math>f \star g</math> are identical in this example.
<!--Note that g∗f and f∗g would be identical even without the symmetry of f, so please don't change the statement above.-->]]

'''Autocorrelation''', sometimes known as '''serial correlation''' in the [[discrete time]] case, measures the [[correlation]] of a [[Signal (information theory)|signal]] with a delayed copy of itself. Essentially, it quantifies the similarity between observations of a [[random variable]] at different points in time. The analysis of autocorrelation is a mathematical tool for identifying repeating patterns or hidden [[Periodic function|periodicities]] within a signal obscured by [[noise (signal processing)|noise]]. Autocorrelation is widely used in [[signal processing]], [[time domain]] and [[time series analysis]] to understand the behavior of data over time. 

Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with [[autocovariance]]. 

Various time series models incorporate autocorrelation, such as [[unit root]] processes, [[trend-stationary process]]es, [[autoregressive process]]es, and [[moving average process]]es.