## What Is 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's conceptually similar to the correlation between two different time series, but autocorrelation uses the same time series twice: once in its original form and once lagged one or more time periods.

For example, if it's rainy today, the data suggests that it's more likely to rain tomorrow than if it's clear today. When it comes to investing, a stock might have a strong positive autocorrelation of returns, suggesting that if it's "up" today, it's more likely to be up tomorrow, too.

Naturally, autocorrelation can be a useful tool for traders to utilize; particularly for technical analysts.

### Key Takeaways

- Autocorrelation represents the degree of similarity between a given time series and a lagged version of itself over successive time intervals.
- Autocorrelation measures the relationship between a variable's current value and its past values.
- An autocorrelation of +1 represents a perfect positive correlation, while an autocorrelation of negative 1 represents a perfect negative correlation.
- Technical analysts can use autocorrelation to measure how much influence past prices for a security have on its future price.

#### Autocorrelation

## Understanding Autocorrelation

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.

As a very simple example, take a look at the five percentage values in the chart below. We are comparing them to the column on the right, which contains the same set of values, just moved up one row.

Day | % Gain or Loss | Next Day's % Gain or Loss |

Monday | 10% | 5% |

Tuesday | 5% | -2% |

Wednesday | -2% | -8% |

Thursday | -8% | -5% |

Friday | -5% |

When calculating autocorrelation, the result can range from -1 to +1.

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).

On the other hand, an autocorrelation of -1 represents a 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 can still be a nonlinear relationship between a time series and a lagged version of itself.

### Testing for Autocorrelation

The most common method of test autocorrelation is the Durbin-Watson test. Without getting too technical, the Durbin-Watson is a statistic that detects autocorrelation from a regression analysis.

The Durbin-Watson always produces a test number range from 0 to 4. Values closer to 0 indicate a greater degree of positive correlation, values closer to 4 indicate a greater degree of negative autocorrelation, while values closer to the middle suggest less autocorrelation.

So why is autocorrelation important in financial markets? Simple. Autocorrelation can be applied to thoroughly analyze historical price movements, which investors can then use to predict *future* price movements. Specifically, autocorrelation can be used to determine if a momentum trading strategy makes sense.

## Autocorrelation in Technical Analysis

Autocorrelation can be useful for technical analysis, That's because technical analysis is most concerned with the trends of, and relationships between, security prices using charting techniques. This is in contrast with fundamental analysis, which focuses instead on a company's financial health or management.

Technical analysts can use autocorrelation to figure out how much of an impact past prices for a security have on its future price.

Autocorrelation can help determine if there is a momentum factor at play with a given stock. If a stock with a high positive autocorrelation posts two straight days of big gains, for example, it might be reasonable to expect the stock to rise over the *next t*wo days, as well.

## Example of Autocorrelation

Let’s assume Emma is looking to determine if a stock's returns in her portfolio exhibit autocorrelation; that is, the stock's returns relate to its returns in previous trading sessions.

If the returns exhibit autocorrelation, Emma could characterize it as a momentum stock because past returns seem to influence future returns. Emma runs a regression with the prior trading session's return as the independent variable and the current return as the dependent variable. She finds that returns one day prior have a positive autocorrelation of 0.8.

Since 0.8 is close to +1, past returns seem to be a very good positive predictor of future returns for this particular stock.

Therefore, Emma can adjust her portfolio to take advantage of the autocorrelation, or momentum, by continuing to hold her position or accumulating more shares.