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Autocorrelation (serial correlation) is the correlation of a series of data with itself at some lag. This is an important topic in time series analysis.

Autocorrelation (serial correlation) is the correlation of a series of data with itself at some lag. For example, if a given value were higher than average, it might be more likely than not that the next value would also be higher than average; if so, there is a positive autocorrelation at lag 1.

The autocorrelation for a time series, between times $$s$$ and $$t$$ is defined as:

$$R(s,t) = \frac{E[(X_t - \mu)(X_s - \mu)]}{\sigma_t \sigma_s}$$

where $$E$$ is the expected value operation.

The examination of autocorrelation is central to time series analysis, where it can indicate nonstationarity. Another context where autocorrelation is important is the analysis of residuals from a linear regression model to assess the possibility that a variable has a misspecified functional form.