autocorrelation

thumb|300px|right|Above: A plot of a series of 100 random numbers concealing a sine function. Below: Its [[correlogram plots the autocorrelation function (ACF) of the series on the y-axis for every lag on the x-axis. Peaks occur at lags where the series is highly correlated with itself. Peaks to the right of the initial peak at lag 0 indicate periodicity in the series and help estimate the concealed sine's period.]] thumb|400px|Visual comparison of convolution, cross-correlation, and autocorrelation. For the operations involving function , and assuming the height of 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 is the reason g*f and f \star g are identical in this example.

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