Granger causality is a statistical hypothesis test used to determine if one time series can help forecast another. Introduced in 1969 by Nobel laureate Clive Granger, this test assesses whether patterns in one variable’s past values offer unique information for predicting another variable’s future behavior. It focuses purely on whether one series’ historical data improves the prediction of another, rather than delving into underlying physical mechanisms.
The Principle of Predictive Causality
The core idea behind Granger causality is rooted in forecasting. Imagine trying to predict tomorrow’s stock price. A straightforward approach involves using only the stock’s past performance, such as its prices from the last few days or weeks, to build a predictive model. This method, often called an autoregressive model, relies solely on the historical patterns of the stock itself.
The Granger causality test then introduces a second time series, for example, daily oil prices, into this prediction. It assesses whether incorporating the past values of oil prices significantly improves the accuracy of the stock price forecast, beyond what could be achieved using only the stock’s own history. If the prediction error for stock prices is notably reduced by including oil price data, then oil prices are said to “Granger-cause” stock prices.
This improvement in forecasting ability is the essence of Granger causality. It is a statistical comparison: comparing a model that predicts a variable using only its own past with a model that adds the past of a second variable. If the second model yields a statistically better prediction, the relationship is identified.
Applications Across Disciplines
Granger causality finds widespread application across various scientific fields, helping researchers uncover predictive relationships within time-ordered data. In economics, it is frequently employed to investigate the interplay between macroeconomic indicators. For instance, researchers might use it to determine if past changes in gross domestic product (GDP) growth rates can predict future unemployment rates, or vice versa.
Neuroscience also utilizes Granger causality to understand brain activity. Scientists can analyze recordings from different brain regions, like those obtained through fMRI or EEG, to see if activity in one area consistently precedes and helps predict activity in another. This helps map out the directional influence and functional connectivity within neural networks.
In climatology, the test can shed light on how large-scale climate phenomena influence regional weather patterns. An example includes analyzing whether historical sea surface temperatures, such as those associated with El Niño events, can predict future rainfall patterns in specific geographic areas, like parts of South America or Australia. This allows for better forecasting of climate impacts.
Distinguishing Prediction from True Causation
It is important to understand that “Granger causality” is a specific statistical term that does not equate to “true” or mechanistic causation. The test identifies predictive relationships based on temporal precedence and improved forecasting, not a direct cause-and-effect link in a physical sense. Clive Granger himself acknowledged that the term “causality” could be misleading, suggesting “precedence” or “temporally related” as more accurate descriptions.
The primary limitation is that Granger causality cannot differentiate between a genuine causal relationship and the influence of a third, unobserved variable affecting both series. For example, if one observes that children’s shoe size “Granger-causes” their reading ability, it means larger shoe sizes predict better reading skills. However, this is not because shoe size directly causes improved reading, but because a confounding variable—age—influences both. As children get older, their shoe size increases, and their reading ability generally improves.
This highlights the classic principle that correlation does not imply causation. Granger causality, while more sophisticated than simple correlation by incorporating time, still operates within this constraint. The test merely reveals if one time series provides statistically significant predictive power for another.
Technical Requirements for Analysis
Applying Granger causality effectively requires adherence to specific technical prerequisites for the time series data. First, the test is exclusively designed for time-series data, meaning observations must be collected sequentially over time at regular intervals, such as daily, monthly, or yearly measurements. This temporal ordering is fundamental to its predictive logic.
A second requirement is that the time series must be “stationary.” This means that the statistical properties of the data, such as its average value (mean) and variability (variance), should remain relatively constant over time. Non-stationary data, where properties change drastically, can lead to misleading results.
Finally, a user must determine the “lag selection,” which refers to how many past time periods of each variable should be considered for the prediction. The choice of lag length can influence the test results, and statistical criteria like the Akaike Information Criterion (AIC) or Bayesian Information Criterion (BIC) are commonly used to guide this decision.