# Autocorrelation Explained: Definition, Function, and Testing Methods

> **Definition**
>
> Autocorrelation is the degree of similarity of a variable between two successive time intervals.

Autocorrelation measures how similar a [time series](https://www.investopedia.com/terms/t/timeseries.asp) is to its lagged version over time. 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 rains today, it's more likely to rain tomorrow than if today is clear. 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.

Autocorrelation is a useful tool for traders, especially technical analysts.

### Key Takeaways

*   Autocorrelation measures the relationship between a time series and its past values, which can provide insights into the predictability of future movements based on historical data.  
    
*   In financial markets, autocorrelation can help traders determine if a momentum trading strategy is viable by evaluating if past returns influence future returns.  
    
*   The Durbin-Watson test is a common method for detecting autocorrelation in regression analysis, with results indicating whether positive or negative autocorrelation is present.  
    
*   Autocorrelation is a crucial concept for technical analysis, allowing analysts to understand how past prices impact future security prices and identify trends.  
    
*   Although autocorrelation helps in predicting future price movements, it is most effective when used alongside other statistical analysis tools.

![Autocorrelation](https://www.investopedia.com/thmb/qcL-_1q9TZSlbG39rf8JsZXWbRk=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Autocorrelation-FINAL-3b2d9f40e52d4d85aa399528e7133083.jpg)

*— Investopedia / Jiaqi Zhou*

## How Autocorrelation Works in Time Series Analysis

Autocorrelation, also known as lagged or [serial correlation](https://www.investopedia.com/terms/s/serial-correlation.asp), measures a variable's relationship with its past values. For a simple example, compare five percentage values with those in the right column, shifted up one row.

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

An autocorrelation of +1 indicates a perfect [positive correlation](https://www.investopedia.com/terms/p/positive-correlation.asp), meaning an increase in one series leads to a similar increase in another.

![Positive Autocorrelation](https://www.investopedia.com/thmb/VyG9fIN7ufNIYKrbpRMV-m4jVcU=/1380x0/filters:no_upscale():max_bytes(150000):strip_icc()/1Auto-336e0893344f4ef3abd033cc83ddd93e.PNG)

**

Conversely, an autocorrelation of -1 signifies a perfect [negative correlation](https://www.investopedia.com/terms/n/negative-correlation.asp), where an increase in one series results in a similar decrease in another.

![Negative Autocorrelation](https://www.investopedia.com/thmb/cDus4vNKZL-tiOs3FmVSaNxWhls=/1252x0/filters:no_upscale():max_bytes(150000):strip_icc()/-1auto-96995b5335fa41a3ac51981667d04eb7.PNG)

**

Autocorrelation measures linear relationships, but small autocorrelation can still indicate nonlinear relations between a series and its lagged version.

### Methods for Testing Autocorrelation in Data

The Durbin-Watson test is the most popular method for identifying autocorrelation in [regression analysis](https://www.investopedia.com/terms/r/regression.asp).

The Durbin-Watson always produces a test number range from 0 to 4. Values near 0 show strong positive correlation, values near 4 indicate strong negative correlation, and middle values suggest weak correlation.

### Distinguishing Correlation from Autocorrelation

Correlation measures the relationship between two variables, whereas autocorrelation measures the relationship of a variable with lagged values of itself.

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](https://www.investopedia.com/terms/m/momentum_investing.asp) makes sense.

## Using Autocorrelation for Technical Analysis

Autocorrelation can be useful for [technical analysis](https://www.investopedia.com/terms/t/technicalanalysis.asp), 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](https://www.investopedia.com/terms/m/momentum.asp) 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.

## Practical Example: Applying Autocorrelation to Stocks

Let’s assume Rain is looking to determine if a stock's returns in their [portfolio](https://www.investopedia.com/terms/p/portfolio.asp) exhibit autocorrelation; that is, the stock's returns relate to its returns in previous trading sessions.

If the returns exhibit autocorrelation, Rain could characterize it as a momentum stock because past returns seem to influence future returns. Rain runs a regression with the prior [trading session's](https://www.investopedia.com/terms/t/tradingsession.asp) return as the independent variable and the current return as the dependent variable. They find 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, Rain can adjust their portfolio to take advantage of the autocorrelation, or momentum, by continuing to hold their position or [accumulating](https://www.investopedia.com/terms/a/accumulation.asp) more shares.

## What Is the Difference Between Autocorrelation and Multicollinearity?

Autocorrelation is the degree of correlation of a variable's values over time. Multicollinearity occurs when independent variables are correlated and one can be predicted from the other. An example of autocorrelation includes measuring the weather for a city on June 1 and the weather for the same city on June 5. Multicollinearity measures the correlation of two independent variables, such as a person's height and weight.

## Why Is Autocorrelation Problematic?

Most statistical tests assume the independence of observations. In other words, the occurrence of one tells nothing about the occurrence of the other. Autocorrelation is problematic for most statistical tests because it refers to the lack of independence between values.  

## What Is Autocorrelation Used for?

Autocorrelation can be used in many disciplines but is often seen in technical analysis. Technical analysts evaluate securities to identify trends and make predictions about their future performance based on those trends.

## The Bottom Line

Autocorrelation is the correlation of a time series and its lagged version over time. Although similar to correlation, autocorrelation uses the same time series twice. Financial analysts and traders use autocorrelation to examine historical price movements and predict future ones. Technical analysts use autocorrelation to determine what or how much of an impact historical prices of a security have on its future price. Although a very useful tool, it is often used with other statistical measures in financial analysis.