Autocorrelation in statistics is a mathematical tool that is usually used for analyzing functions or series of values, for example, time domain signals. In other words, autocorrelation determines the presence of correlation between the values of variables that are based on associated aspects. In a way, it is the cross-correlation of a signal with itself. Most of the statistical models are based upon the assumption of instance independence, which gets desecrated by autocorrelation. Autocorrelation is very useful in activities where there are repeated signals. Autocorrelation is used to determine the periodic signals that get obscured beneath the noise, or it is used to realize the fundamental frequency of a signal that does not have that frequency as a component but applies it there along with many harmonic frequencies.
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In statistics, the correlation of a method against a time-shifted version is the autocorrelation of a discrete time series method. There are many applications where autocorrelation is very useful. Autocorrelation is used for the measurement of the optical spectra, and for the measurements of minutely lived light pulses that are produced by lasers. This is done with the help of optical autocorrelators. Autocorrelation is used in optics, where the normalized autocorrelations and cross correlations together give the degree of coherence of an electromagnetic field. Autocorrelation is also used for signal processing. Autocorrelation can help you get information about repetitive events like musical beats or pulsar frequencies, but it can still not give the position in time of the beats. Thus, autocorrelation can be used for identifying non-randomness in data and to classify an appropriate time series model for the non random data.
In other words it can be said that autocorrelation is a correlation coefficient, where the correlation is not between the two different variables. Rather, it is between the different values of the same variables. When autocorrelation is used to spot non–randomness, it is mostly the autocorrelation of the first lag that is taken into consideration. Autocorrelation used to determine a proper time series model is conventionally plotted for various lags.
Thus, we can say that autocorrelation is useful for answering two main questions:
1. Was what was generated taken from a random process or a non–random process?
2. Which model is a more appropriate model for the generated data?
Autocorrelation has many properties and it is used for diverse studies and diverse dimensions. The properties of autocorrelation are interchangeable in different dimensions. The most important quality of autocorrelation is symmetry and consistency. Autocorrelation for periodic functions is also periodic, with a similar period. If the functions are completely uncorrelated, then their autocorrelation is the sum of the autocorrelations of each function separately. Autocorrelation is a unique kind of cross correlation, and thus it bears all the properties of cross correlation. The autocorrelation function is easily available is general statistical software programs, thus one can easily access autocorrelation.
