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

Autocorrelation 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 inform sources of non-stationarity. Another context where autocorrelations are important is the analysis of residuals from a linear regression model to assess the possibility that a variable has a misspecified functional form.

history | excerpt history