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Autocorrelation typically occurs in a set of data in which patterns repeat. The values of similar variables, such as income or economic data, for example, are often correlated with one another. Researchers can also come upon autocorrelation by accident. It often appears in studies of economics, scientific experiments involving signal processing, as well as in optics and the recording of music. Usually described in conjunction with a time series, the phenomenon comprises several patterns which researchers use to analyze or group data.
There is usually synchronization between the two variables for autocorrelation to occur. An example is if the income of one person changes, and at the same time this cash flow can alter how another person or group spends during that period. Data can also be autocorrelated if a strike by a company or labor union reduces work output at one time, and the trend continues into another measured timeframe. Partial autocorrelation is sometimes possible; there can be a lag if data are correlated within one series over time. Serial autocorrelation is typically when the lag occurs between different data in a time series.
Patterns that often occur with autocorrelation can be represented by the patterns of curves on a graph. These curves can be used to reflect a trend; this sometimes includes upward and downward patterns that may occur in cycles. Mistakes in calculations can also cause data to correlate in error, such as if a novice researcher uses the wrong values or variables. The use of extrapolation and interpolation of data sometimes correlates them, while not doing so keeps variables separate in relation to time.
Autocorrelation can have a positive value, especially if the trend in a pattern is moving up. Downward trends are often reflected by a negative value. Such patterns are often analyzed in economics, but can also show up in mathematical analyses of signal pulses, electromagnetic fields, as well as in the various applications of statistics. The phenomenon is often used in such diverse applications as measuring the positions of atoms, as well as studying the distribution of galaxies in the universe.
Detection of autocorrelation is typically performed using the Durbin Watson test. A statistic is mathematically measured and whether a value is above or below that of another variable typically determines the result. Researchers can then determine the purity, and if this characteristic is found, the dataset is often returned to its original form to remove the phenomenon if possible.
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