Granger causality

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Granger causality is a statistical concept used to determine if one time series is useful in forecasting another. Although it is named "causality," it is important to note that Granger causality does not imply true causal relationship in the philosophical sense, but rather indicates a predictive relationship between two datasets. The concept was introduced by the econometrician Clive Granger in 1969, for which he was awarded the Nobel Prize in Economic Sciences in 2003, shared with Robert Engle for their contributions to the analysis of time series data with time-varying volatility (ARCH models).

Definition

Granger causality tests whether past values of one variable help to predict the future value of another variable, while controlling for the past values of the forecasted variable itself. Mathematically, a variable X is said to Granger-cause Y if, given the past values of Y, past values of X are useful for predicting Y. If X Granger-causes Y, it does not necessarily mean that X causes Y in a direct or causal way, but rather that X can be used to forecast Y better than using the past values of Y alone.

Methodology

The most common approach to test for Granger causality is through a series of F-tests in the context of a Vector Autoregression (VAR) model, where the lagged values of both X and Y variables are used as predictors in the regression model. The null hypothesis is that the coefficients of the lagged values of the causing variable (X in the case where we test if X Granger-causes Y) are all zero. Rejection of the null hypothesis indicates that the lagged values of X do indeed have predictive power for Y, suggesting Granger causality.

Applications

Granger causality has been widely applied in various fields such as Economics, Neuroscience, and Environmental Science, among others. In economics, it is used to understand the relationship between economic indicators, such as whether money supply Granger-causes inflation. In neuroscience, it can help in understanding the directional information flow between different regions of the brain. Environmental scientists use it to study the relationship between human activities and climate change.

Limitations

It is crucial to understand the limitations of Granger causality. The test assumes that the time series data is stationary, meaning that the statistical properties of the series do not change over time. Additionally, the presence of a third, unobserved variable that influences both the predictor and the outcome can lead to spurious results. Lastly, the Granger causality test does not provide information on the actual mechanism or the nature of the relationship between the variables.

See Also

• Time Series Analysis
• Econometrics
• Vector Autoregression (VAR)
• F-test
• Stationarity

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