Autocorrelation, denoted \( { \rho_k } \), is a measure of the correlation of a particular time series with the same time series delayed by k lags (the distance between the observations that are so correlated). It is obtained by dividing the covariance between two observations, separated by k lags, of a time series (autocovariance) by the standard deviation of y t and y t − k . If the autocorrelation is calculated for all values of k we obtain the autocorrelation function. For a time series that does not change over time, the autocorrelation function decreases exponentially to 0.
HISTORY
The first research into autocorrelation, the partial autocorrelation and the correlogram was performed in the 1920s and 1930s by Yule, George, who developed the theory of autoregressive processes.
MATHEMATICAL ASPECTS
We define the autocorrelation of time series Y t by:
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Bourbonnais, R.: Econométrie, manuel et exercices corrigés, 2nd edn. Dunod, Paris (1998)
Box, G.E.P., Jenkins, G.M.: Time Series Analysis: Forecasting and Control (Series in Time Series Analysis). Holden Day, San Francisco (1970)
Chatfield, C.: The Analysis of Time Series: An Introduction, 4th edn. Chapman & Hall (1989)
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© 2008 Springer-Verlag
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(2008). Autocorrelation. In: The Concise Encyclopedia of Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32833-1_17
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DOI: https://doi.org/10.1007/978-0-387-32833-1_17
Publisher Name: Springer, New York, NY
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