Granger causality and block exogeneity tests for vector autoregression (VAR) models
The gctest
object function can conduct leave-one-out,
exclude-all, and block-wise Granger causality tests for the
response variables of a fully specified vector autoregression (VAR)
model (represented by a varm
model object).
To conduct a block-wise Granger causality test from specified sets of time series data
representing "cause" and "effect" multivariate response variables, or to address possibly
integrated series for the test, see the gctest
function.
returns
the test decision h
= gctest(Mdl
)h
from conducting leave-one-out Granger causality tests on all
response variables that compose the VAR(p) model
Mdl
.
uses additional options specified by one or more name-value pair arguments. For example,
h
= gctest(Mdl
,Name,Value
)'Type',"block-wise",'Cause',1:2,'Effect',3:5
specifies conducting a
block-wise test to assess whether the response variables
Mdl.SeriesNames(1:2)
Granger-cause the response variables
Mdl.SeriesNames(3:5)
conditioned on all other variables in the
model.
gctest
uses the series names in Mdl
in
test result summaries. To make the output more meaningful for your application, specify
series names by setting the SeriesNames
property of the VAR model
object Mdl
by using dot notation before calling
gctest
. For example, the following code assigns names to the
variables in the 3-D VAR model object
Mdl
:
Mdl.SeriesNames = ["rGDP" "m1sl" "inflation"];
The exclude-all and leave-one-out Granger causality tests conduct multiple,
simultaneous tests. To control the inevitable increase in the false discovery rate,
decrease the level of significance Alpha
when you conduct multiple
tests. For example, to achieve a family-wise significance level of 0.05, specify
'Alpha',0.05/numtests
.
The name-value pair arguments Cause
and Effect
apply to the block-wise Granger causality test because they specify which equations have lag
coefficients set to 0 for the null hypothesis. Because the leave-one-out and exclude-all
Granger causality tests cycle through all combinations of variables in the VAR model, the
information provided by Cause
and Effect
is not
necessary. However, you can specify a leave-one-out or exclude-all Granger causality test and
the Cause
and Effect
variables to conduct unusual
tests such as constraints on self lags. For example, the following code assesses the null
hypothesis that the first variable in the VAR model Mdl
is not the 1-step
Granger-cause of
itself:
gctest(Mdl,'Type',"leave-one-out",'Cause',1,'Effect',1);
[1] Granger, C. W. J. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods." Econometrica. Vol. 37, 1969, pp. 424–459.
[2] Hamilton, James. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[3] Dolado, J. J., and H. Lütkepohl. "Making Wald Tests Work for Cointegrated VAR Systems." Econometric Reviews. Vol. 15, 1996, pp. 369–386.
[4] Lütkepohl, H. New Introduction to Multiple Time Series Analysis. New York, NY: Springer-Verlag, 2007.
[5] Toda, H. Y., and T. Yamamoto. "Statistical Inferences in Vector Autoregressions with Possibly Integrated Processes." Journal of Econometrics. Vol. 66, 1995, pp. 225–250.