For example, if it rains today, the data shows that it is more likely to rain tomorrow than if it is sunny today. In investing terms, a stock's returns may exhibit strong positive autocorrelation, meaning that if it "goes up" today, it's more likely to go up tomorrow too.

Naturally, autocorrelation can be a useful tool for traders, especially technical analysts.

Key Points

• Autocorrelation represents the similarity between a given time series and its delayed version over a continuous time interval.
• Autocorrelation measures the relationship between the current value of a variable and its past values.
• An autocorrelation of +1 indicates a perfect positive correlation, while -1 indicates a perfect negative correlation.
• Technical analysts can use autocorrelation to measure the impact of past prices on a security's future prices.

Understanding autocorrelation

Autocorrelation may also be called lagged correlation or serial correlation because it measures the relationship between the current value of a variable and its past values.

As a very simple example, the table below shows five percentage values. We compare these values ​​to the same data on the right, with the values ​​in that column just moved up one row.

The result of calculating autocorrelation can fluctuate between -1 and +1.

An autocorrelation of +1 indicates a perfect positive correlation (an observed increase in one time series leads to a corresponding increase in the other).

On the other hand, an autocorrelation of -1 indicates a perfect negative correlation (an observed increase in one time series leads to a corresponding decrease in the other).

Autocorrelation measures a linear relationship. Even if the autocorrelation value is small, there may still be a non-linear relationship between the time series and its delayed version.

The most common way to test for autocorrelation is the Durbin-Watson test. Simply put, Durbin-Watson is a statistic used to detect autocorrelation through regression analysis.

Durbin-Watson test results always range from 0 to 4. Values ​​closer to 0 indicate greater positive correlation, values ​​closer to 4 indicate greater negative autocorrelation, and values ​​closer to the middle indicate smaller autocorrelation.

The difference between correlation and autocorrelation: Correlation measures the relationship between two variables, while autocorrelation measures the relationship between a variable and its delayed value.

So why is autocorrelation important in financial markets? The reason is simple. Autocorrelation can be used to deeply analyze historical price changes, and investors can use this to predict future price changes. Specifically, autocorrelation can be used to determine whether a momentum trading strategy makes sense.

Application of autocorrelation in technical analysis

Autocorrelation is very useful for technical analysis, which focuses on trends in security prices and the relationships between them, using charting techniques. This is in contrast to fundamental analysis, which focuses on a company's financial health or management.

Technical analysts can use autocorrelation to evaluate the impact of past security prices on future prices.

Autocorrelation can help determine whether a stock has a momentum factor. For example, if a stock with high positive autocorrelation has risen sharply for two consecutive days, a reasonable expectation is that the stock will also rise over the next two days.

Examples of autocorrelation

Suppose Rain wants to determine whether the returns of a stock in his portfolio exhibit autocorrelation; that is, the stock's returns are related to returns in previous trading periods.

If returns exhibit autocorrelation, Rain could consider it a momentum stock because past returns appear to influence future returns. Rain performs a regression analysis, using the previous trading period's return as the independent variable and the current return as the dependent variable. They find that the previous day's returns have a positive autocorrelation of 0.8.

Since 0.8 is close to +1, past returns appear to be a very good positive predictor of the stock's future returns.

Therefore, Rain can adjust his portfolio to take advantage of autocorrelation or momentum, continuing to hold the stock or adding more holdings.

What is the difference between autocorrelation and multicollinearity?

Autocorrelation is the degree to which a variable's values ​​are correlated over time. Multicollinearity occurs when there is a correlation between independent variables, and one variable can be predicted by another variable. An example of autocorrelation would include measuring the weather in one city on June 1st versus the weather in the same city on June 5th. Multicollinearity, on the other hand, measures the correlation between two independent variables, such as a person's height and weight.

Why is autocorrelation a problem?

Most statistical tests assume that observations are independent of each other. In other words, the occurrence of one observation does not explain the occurrence of another observation. Autocorrelation is a problem for most statistical tests because it involves a lack of independence between values.

What are the applications of autocorrelation?

Autocorrelation can be applied to many disciplines, but is most commonly found in technical analysis. Technical analysts evaluate securities to identify trends and predict their future performance.

Summary

Autocorrelation is the time-varying correlation between a time series and its delayed version. Although similar to correlation, autocorrelation uses the same time series twice. Financial analysts and traders use autocorrelation to study historical price movements and predict future trends. Technical analysts use autocorrelation to determine the impact of historical security prices on future prices. Although autocorrelation is a very useful tool, it is often used in conjunction with other statistical indicators in financial analysis.

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