Autocorrelation

Autocorrelation is a mathematical representation of the degree of similarity between a given time series and a lagged version of itself over successive time intervals. It is the same as calculating the correlation between two different time series, except that the same time series is actually used twice: once in its original form and once lagged one or more time periods.

Autocorrelation can also be referred to as lagged correlation or serial correlation, as it measures the relationship between a variable's current value and its past values. When computing autocorrelation, the resulting output can range from 1 to negative 1, in line with the traditional correlation statistic. An autocorrelation of +1 represents a perfect positive correlation (an increase seen in one time series leads to a proportionate increase in the other time series). An autocorrelation of negative 1, on the other hand, represents perfect negative correlation (an increase seen in one time series results in a proportionate decrease in the other time series). Autocorrelation measures linear relationships; even if the autocorrelation is minuscule, there may still be a nonlinear relationship between a time series and a lagged version of itself.

Autocorrelation can be useful for technical analysis, which is most concerned with the trends of, and relationships between, security prices using charting techniques in lieu of a company's financial health or management. Technical analysts can use autocorrelation to see how much of an impact past prices for a security have on its future price.

Autocorrelation can show if there is a momentum factor associated with a stock. For example, if you know that a stock historically has a high positive autocorrelation value and you witnessed the stock making solid gains over the past several days, then you might reasonably expect the movements over the upcoming several days (the leading time series) to match those of the lagging time series and to move upward.

Assume an investor is looking to discern if a stock's returns in her portfolio exhibit autocorrelation; the stock's returns are related to its returns in previous trading sessions. If the returns do exhibit autocorrelation, the stock could be characterized as a momentum stock; its past returns seem to influence its future returns. The investor runs a regression with two prior trading sessions' returns as the independent variables and the current return as the dependent variable. She finds that returns one day prior have a positive autocorrelation of 0.7, while the returns two days prior have a positive autocorrelation of 0.3. Past returns seem to influence future returns, and she can adjust her portfolio to take advantage of the autocorrelation and resulting momentum.