The Granger causality tests if one variable “Granger causes” another variable and vice versa, using restricted autoregressive lags and unrestricted distributive lag models. Typically, predictive causality in finance and economics is tested by measuring the ability to predict the future values of a time series using prior values of another time series. A simpler definition might be that a time-series variable A can Granger cause another time-series variable B if predictions of the value of B based solely on its own prior values and on the prior values of A are comparatively better than predictions of B based solely on its own past values. For example, Figure 9.49 illustrates two time-series variables, A and B. The two null hypotheses tested are that there is no Granger causality of A on B and also between B and A. We see that the p-values for both directions are greater than an alpha of 0.05, so we cannot reject the null hypothesis and conclude that neither A Granger causes B nor B Granger causes A, when both are lagged for 3 periods (this is the value 3 in the input box).
The Granger causality model can only be run pairwise and assumes that the time-series variable is stationary or not stochastic. If a time-series is suspected to have nonstationary effects, we can run the Augmented Dickey–Fuller test (see Figure 9.50), where the null hypothesis is that the series is nonstationary, has a unit root, or I(1) process, and is potentially stochastic. The example BizStats results indicate that the variable is stationary (the null hypothesis is rejected with a p-value of 0.0442).
However, if a time-series variable is nonstationary and stochastic, you can still attempt to forecast this series in several ways:
Figure 9.49: Granger Causality
Figure 9.50: Augmented Dickey–Fuller Test for Stationarity
Figure 9.51: Stochastic Processes
Figure 9.52: Error Correction Model
Figure 9.53: Hodrick–Prescott Filtering