### 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 in autocorrelation, the same time series is used twice: once in its original form and once lagged one or more time periods.

For instance, if it’s rainy today, the data suggests that it’s more likely to rain tomorrow than if it’s clear today. In the realm of 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 as well.

Autocorrelation is particularly useful for traders, especially 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.
- It 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 -1 represents a perfect negative correlation.
- Technical analysts use autocorrelation to gauge how much influence past prices for a security have on its future price.

### Understanding Autocorrelation

Autocorrelation, also known as lagged correlation or serial correlation, measures the relationship between a variable’s current value and its past values.

Consider this example with five percentage values:

|———–|—————-|————————–| | 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 ranges from -1 to +1, where:

- +1 indicates a perfect positive correlation (an increase in one time series leads to a proportionate increase in the other).
- -1 indicates a perfect negative correlation (an increase in one time series results in a proportionate decrease in the other).

Autocorrelation primarily measures linear relationships, but even small autocorrelation values can indicate non-linear relationships.

### Autocorrelation Tests

The most common method to test autocorrelation is the Durbin-Watson test. The Durbin-Watson statistic, derived from a regression analysis, detects autocorrelation in the residuals. Values closer to 0 indicate a greater degree of positive correlation, while values closer to 4 indicate a greater degree of negative autocorrelation. Values near the middle suggest less autocorrelation.

### Correlation vs. Autocorrelation

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

In financial markets, autocorrelation helps analyze historical price movements to predict future price movements. It is particularly useful for determining if a momentum trading strategy makes sense.

### Autocorrelation in Technical Analysis

Autocorrelation is valuable for technical analysis, which focuses on the trends and relationships between security prices using charting techniques. Unlike fundamental analysis, which looks at a company’s financial health, technical analysts use autocorrelation to observe what impact past prices have on future prices. This can reveal momentum factors, allowing for more informed trading decisions.

### Example of Autocorrelation

Let’s assume you’re looking to determine if a stock in your portfolio exhibits autocorrelation. If the stock’s returns in previous trading sessions relate to future returns, it could be characterized as a momentum stock.

You run a regression with the prior trading session’s return as the independent variable and the current return as the dependent variable. A positive autocorrelation of 0.8 suggests that past returns are good predictors of future returns. You might then adjust your portfolio to take advantage of this momentum by holding or accumulating more shares.

### Difference Between Autocorrelation and Multicollinearity

Autocorrelation refers to the correlation of a variable’s values over time. Multicollinearity occurs when independent variables are correlated and one can be predicted from the other.

### Why Is Autocorrelation Problematic?

Most statistical tests assume the independence of observations. Autocorrelation is problematic as it violates this assumption, implying a lack of independence between values.

### What Is Autocorrelation Used For?

Autocorrelation is widely used in technical analysis for evaluating securities and identifying trends. It helps predict future performance based on historical trends.

### The Bottom Line

Autocorrelation analyzes the correlation of a time series with its lagged version over time. It is used by financial analysts and traders to predict future price movements based on historical data. Although it’s highly useful, it is often combined with other statistical measures for comprehensive financial analysis.

**Related Terms:** Correlation, Serial Correlation, Momentum Investing, Regression Analysis.