What is Granger causality

Introduction

Granger causality is a statistical technique that helps to determine whether one time series is useful in forecasting another time series. It is a powerful tool used widely in economics, neuroscience, physics, climate modeling, and other branches of science. Granger causality allows us to determine whether one signal can be used to predict another signal, making it a valuable and informative technique for data analysis.

History

Granger causality was first introduced by the Nobel Prize-winning economist Clive Granger in 1969. Granger's work centered around the notion that the past of a time series could contain valuable information about the future of that time series or other related time series. With this in mind, Granger developed a statistical model that could help to determine the causal relationships between two or more time series.

The Basic Idea

The basic idea behind Granger causality is that if a time series X can help to predict a time series Y, then X is said to Granger-cause Y. However, this does not mean that X is the only cause of Y, nor does it mean that the relationship between X and Y is necessarily causal. Instead, Granger causality is a statistical tool that can help to uncover statistically significant relationships between two or more time series.

How Granger Causality Works

To understand how Granger causality works, it is important to first understand what a time series is. A time series is a sequence of values that are recorded over time. For example, stock market prices, weather patterns, and physiological signals such as heart rate or blood pressure can all be recorded as time series.

Granger causality involves comparing two time series, X and Y, to see whether one can help to predict the other. This is done by constructing a statistical model that uses past values of X and Y to predict future values of Y. If the model with X as a predictor performs better than the model without X, then we can say that X Granger-causes Y.

Granger Causality vs. Correlation

It is important to note that Granger causality is not the same as correlation. Correlation measures the strength of the linear relationship between two variables, whereas Granger causality measures the extent to which one variable can help to predict another.

For example, heating oil prices and ice cream sales may be highly correlated, but one does not cause the other. Instead, both variables are affected by a third variable - the weather. However, if we were to compare heating oil prices and ice cream sales over time and find that heating oil prices help to predict ice cream sales, then we could say that heating oil prices Granger-cause ice cream sales.

Applications of Granger Causality

Granger causality has many practical applications. In economics, it is used to model relationships between variables such as interest rates, stock prices, and inflation. In neuroscience, it can be used to model the interactions between different regions of the brain. In physics, it can be used to model the interactions between particles or waves. In climate modeling, it can be used to model the interactions between different environmental factors.

Limitations of Granger Causality

There are some limitations to using Granger causality. One limitation is that it assumes that the time series are stationary, meaning that their statistical properties do not change over time. In real-world applications, this is often not the case, and therefore additional methods may be needed to account for non-stationarity.

Another limitation is that the technique assumes that the relationship between the time series is linear. If the relationship is non-linear, then Granger causality may not be able to detect it.

Conclusion

Granger causality is a powerful statistical technique that can be used to model the causal relationships between two or more time series. It has many applications in economics, neuroscience, physics, climate modeling, and other branches of science. However, it is important to be aware of the limitations of the technique, and to use additional methods if necessary to account for non-stationarity and non-linear relationships.