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Granger Causality Test
Statistical test developed by Clive Granger to determine whether one time series contains predictive information about another future time series. This test is based on the hypothesis that knowledge of past values of a variable X improves the prediction of a variable Y beyond what is possible with only the past values of Y.
Linear prediction
Forecasting method that uses a linear combination of past values of one or more variables to estimate future values. The classical Granger test relies on linear prediction models to evaluate causality relationships between time series.
Time lag
Temporal delay between a cause and its effect, represented by the number of past periods used to predict future values in causality models. The appropriate choice of lag is crucial for the validity of the Granger test and can be determined by information criteria such as AIC or BIC.
Granger F-test
Specific version of the Granger test using the F-statistic to compare two regression models: a restricted model (without the supposed causal variable) and an unrestricted model (with this variable). The nullity of the coefficients of the causal variable in the restricted model is tested against their non-nullity in the complete model.
Integration
Order of integration of a time series, denoted I(d), indicating the number of times the series must be differenced to become stationary. Knowledge of the order of integration is fundamental for correctly applying Granger tests and avoiding spurious regressions.
Multivariate causality test
Extension of the Granger test to the case of multiple simultaneous variables, using VAR (Vector Autoregressive) models to analyze causality relationships in a complex system. This approach allows controlling for the effects of other variables and identifying direct causality relationships.
Instantaneous Granger test
Causality test that examines whether simultaneous changes in two variables at the same time period are statistically significant, unlike the classical Granger test which focuses on time lags. This test is particularly relevant for high-frequency data where instantaneous effects can be important.
Akaike Information Criterion (AIC)
Statistical metric used to select the optimal number of lags in Granger test models, balancing model fit and complexity. The AIC penalizes complexity less severely than the BIC, tending to select models with more parameters.
Bayesian Information Criterion (BIC)
Model selection criterion for determining the optimal number of lags in Granger tests, favoring parsimony over AIC. The BIC imposes a stronger penalty for additional parameters, reducing the risk of overfitting in causality models.
VAR Model (Vector Autoregressive)
Econometric model where each variable is regressed on its own past values and on the past values of other variables in the system, the basis for multivariate Granger causality tests. VAR models capture dynamic interdependencies between multiple time series.
Impulse-Responses
Complementary analysis to Granger tests that traces the evolution of variables over time following a shock to a specific variable in a VAR model. This technique quantifies the magnitude and duration of causality effects identified by Granger tests.
Variance Decomposition
Statistical method that determines the proportion of forecast error variance of a variable attributable to shocks to itself and to other variables in the system. This analysis quantifies the relative importance of Granger causality relationships in explaining variations in variables.
Non-linearity Test
Extension of Granger tests to non-linear relationships between time series, using models such as neural networks or regime-switching models. These tests detect causalities that classical linear tests might miss.
Conditional Causality
Granger test that evaluates the causality relationship between two variables while conditioning on a set of control variables, thereby isolating the direct causality effect. This approach distinguishes direct causality from indirect causality mediated by other variables.
Non-linear Granger Test
Variant of the Granger test designed to detect non-linear predictive relationships between time series, using methods such as threshold models or kernels. This test is particularly useful when economic relationships exhibit asymmetries or regime changes.