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 re
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.
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).