[R-sig-finance] Puzzled on a granger causality situation
Ajay Narottam Shah
ajayshah at mayin.org
Thu Aug 11 07:28:46 CEST 2005
This is not really an R question, but it will be great if someone can
help me understand the situation it will be great. :-)
I am doing a simple granger causality test in a bivariate setting,
with two variables named "fii" and "rM".
On one hand, when I use grangertest() from lmtest, I get:
Model 1: fii ~ Lags(fii, 1:5) + Lags(rM, 1:5)
Model 2: fii ~ Lags(fii, 1:5)
Res.Df Df F Pr(>F)
1 634
2 639 5 2.5439 0.02718 *
Model 1: rM ~ Lags(rM, 1:5) + Lags(fii, 1:5)
Model 2: rM ~ Lags(rM, 1:5)
Res.Df Df F Pr(>F)
1 634
2 639 5 1.2481 0.2850
which seems to suggest that `rM' does granger-cause `fii' but not the
over way around.
But, when I look at OLS estimates of a model explaining `rM', I get
something different. I am using the variable names like `rM.l2' for
"rM lagged by 2", and so on.
Call:
lm(formula = rM ~ rM.l1 + rM.l2 + rM.l3 + rM.l4 + rM.l5 + fii.l1 +
fii.l2 + fii.l3 + fii.l4 + fii.l5)
Residuals:
Min 1Q Median 3Q Max
-11.0345 -0.7043 0.1124 0.8122 8.1185
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 8.914e-02 6.871e-02 1.297 0.19499
rM.l1 1.199e-01 4.034e-02 2.972 0.00307 **
rM.l2 -1.618e-01 4.077e-02 -3.969 8.03e-05 ***
rM.l3 5.857e-02 4.124e-02 1.420 0.15601
rM.l4 7.337e-02 4.070e-02 1.803 0.07192 .
rM.l5 -4.726e-02 4.065e-02 -1.163 0.24546
fii.l1 3.785e-04 1.874e-04 2.019 0.04389 *
fii.l2 8.979e-05 1.909e-04 0.470 0.63822
fii.l3 -6.184e-05 1.890e-04 -0.327 0.74366
fii.l4 1.075e-04 1.902e-04 0.565 0.57218
fii.l5 -2.272e-04 1.858e-04 -1.223 0.22186
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.388 on 634 degrees of freedom
Multiple R-Squared: 0.05906, Adjusted R-squared: 0.04422
F-statistic: 3.98 on 10 and 634 DF, p-value: 2.707e-05
Here I see that the coefficient of fii.l1 is teetering on the edge of
significance (t=2.019).
My question is: Why is it that grangertest(), which is a joint test
of fii.l1=fii.l2=fii.l3=fii.l4=fii.l5=0, giving a different answer
from just looking at the coefficient fii.l1?
Finally, an R question: in the context of lm(), how does one do a test
of a set of general linear restrictions?
--
Ajay Shah Consultant
ajayshah at mayin.org Department of Economic Affairs
http://www.mayin.org/ajayshah Ministry of Finance, New Delhi
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