Granger Causality Test

The Granger causality test checks whether past values of one time series improve the prediction of another series beyond what the second series' own past values provide.

Granger 인과성 검정은 한 시계열의 과거 값이 다른 시계열 자신의 과거 값만으로 하는 예측을 더 개선하는지를 검정하는 방법이다.

How do I test whether one time series helps predict another?

한 시계열이 다른 시계열을 예측하는 데 도움이 되는지 어떻게 검정하나요?

The Granger causality test compares a model of Y using its own lags with a model that also includes lags of X, and a significant improvement means X Granger-causes Y. It fits stationary time series or a VAR framework, and it establishes predictive precedence rather than true causation.

When to use Granger Causality Test

• Two or more stationary time series observed at regular intervals
• Testing the direction of predictive relationships, including bidirectional effects
• Follow-up tests within a fitted VAR or VECM

When to use something else

• You need a causal effect of an intervention: use interrupted time series or difference-in-differences
• Series are nonstationary and integrated: use the Toda–Yamamoto procedure or test within a VECM

Assumptions and requirements

• Stationary series or appropriate differencing
• Appropriate lag length
• No omitted variables that drive both series
• Uncorrelated residuals

What the analysis reports

• F or chi-square (Wald) statistic for each direction
• p-values
• Selected lag order
• Underlying VAR coefficients

How to report it

Lagged values of [X] significantly improved the prediction of [Y], F([df1], [df2]) = [value], p = [value], indicating that [X] Granger-causes [Y].

Related methods

• Vector Autoregression (VAR)
• Vector Error Correction Model (VECM)
• Transfer Entropy

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