GRANGER CAUSALITY TEST SERIES
Dots in the lower left quadrant (close to the origin) correspond to series where Granger-causality is found by both traditional and robust tests. Dots in the upper right quadrant correspond to series where no Granger-causality is found by either traditional tests or by Granger-causality tests robust to instabilities. The dotted lines represent p-values of 5%, and divide the picture in four quadrants. Each dot in the figure corresponds to one of the series that we consider. Panel A in Figure 21.1 reports results for forecasting inflation and Panel B for output growth.
To get a sense of how important instabilities are, Figure 21.1 reports scatterplots of the p-values of the traditional Granger-causality tests (on the horizontal axis) and of Rossi’s (2005) Granger-causality test robust to instabilities (on the vertical axis). For example, only selected interest rates Granger-cause inflation, although almost all interest rates do Granger-cause inflation if we take instabilities into account. Second, in several cases traditional Granger-causality tests do not find predictive ability whereas Rossi’s (2005) test does, thus indicating that there is Granger-causality once instability has been taken into account. For example, inflation does not Granger-cause output growth in most countries, but some measures of unemployment do. The table show which predictors are most useful. First, the traditional Granger-causality tests show that many of the predictors that we consider do help predicting both inflation and output growth since, in most cases, the p-values are close to zero. 56 The table shows two interesting empirical results. For each of the predictors that we consider (reported in the first column), transformed in several possible ways (described in the second column), and for each of the countries that we consider (described in the remaining columns), the table reports p-values of traditional Granger-causality tests (upper row) and p-values of Rossi’s (2005) Granger-causality test robust to instabilities (lower row, in parentheses), QLR T ∗, defined in Eq. Table 1 reports results of Granger-causality tests as well as Rossi’s (2005) Granger-causality tests robust to instabilities. All rights reserved.Barbara Rossi, in Handbook of Economic Forecasting, 2013 4.1.1 Do Traditional Macroeconomic Time Series Granger-Cause Inflation and Output Growth? All these results indicate that REST-GCA may be useful toolkit for caudal analysis of fMRI data.Ĭopyright © 2011 Elsevier B.V. One sample t-tests on the signed-path coefficients showed positive causal effect from rFIC to dACC but negative from dACC to rFIC. The results of one sample t-tests on Z score showed bi-directional positive causal effect between rFIC and the dorsal anterior cingulate cortex (dACC). Using Jarque-Bera goodness-of-fit test and the Lilliefors goodness-of-fit test, we found that the transformation from F to F' and the further standardization from F' to Z score substantially improved the normality.
Using REST-GCA, we tested the causal effect of the right frontal-insular cortex (rFIC) onto each voxel in the whole brain, and vice versa, each voxel in the whole brain on the rFIC, in a voxel-wise way in a resting-state fMRI dataset from 30 healthy college students. REST-GCA also intergrates a programme that could transform the distribution of residual-based F to approximately normal distribution and then permit parametric statistical inference at group level. This toolkit, namely REST-GCA, could output both the residual-based F and the signed-path coefficient. Based on another MATLAB GUI toolkit, Resting State fMRI Data Analysis Toolkit (REST), we implemented GCA on MATLAB as a graphical user interface (GUI) toolkit. A lot of functional magnetic resonance imaging (fMRI) studies have indicated that Granger causality analysis (GCA) is a suitable method to reveal causal effect among brain regions.
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