Autocorrelation

Definition:

Autocorrelation is the measure we calculate to find out to which degree we can correlate a variable to its past values. It is synonymous to “negative mean reversion. Moreover, AC for a time lag of one period is given by:

$ AC(\rho _{t},\rho _{t-1})= \frac{Cov(\rho _{t},\rho _{t-1})}{\sigma(\rho _{t})\sigma(\rho _{t-1})} $

AC: autocorrelation
pt: correlation values for time period t
pt-1: correlation values for time period t − 1
Cov: covariance

Example of Autocorrelation

Let's suppose an analyst was to predict oil prices. If it exists in the series, it means that we can use the past values of the oil series to model future values. If there isn’t any autocorrelation present, it would be difficult to predict the oil prices using the time series models.