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 re
Article
26 sectionsContents
- Autocorrelation of stochastic processes
- Definition for wide-sense stationary stochastic process
- Normalization
- Properties
- Symmetry property
- Maximum at zero
- Cauchy–Schwarz inequality
- Autocorrelation of white noise
- Wiener–Khinchin theorem
- Autocorrelation of random vectors{{anchor|Matrix}}
- Properties of the autocorrelation matrix
- Autocorrelation of deterministic signals
- Autocorrelation of continuous-time signal
- Autocorrelation of discrete-time signal
- Definition for periodic signals
- Properties
- Multi-dimensional autocorrelation
- Efficient computation
- Estimation
- Hassani −1/2 theorem
- Regression analysis
- Applications
- Serial dependence
- See also
- References
- Further reading
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.