[R-SIG-Finance] cointegration and causality test
Pfaff, Bernhard Dr.
Bernhard_Pfaff at fra.invesco.com
Tue Apr 29 10:08:08 CEST 2008
Hello Bereket,
you might find this article of interest:
http://edoc.hu-berlin.de/series/sfb-373-papers/1999-4/PDF/4.pdf
The section on causality adresses your problem. You might find the
function cajorls() helpful in this context. Furthermore, if you want to
analyse your cointegration vector in more detail, have a look at the
functions: alrtest(), ablrtest() and blrtest().
Best,
Bernhard
>Dear All,
>I am doing cointegration and causality test among four variables. I
>performed the cointegration test using ca.jo() function and
>the result of
>trace test is:
> test 10pct 5pct 1pct
>r <= 3 | 2.76 7.52 9.24 12.97
>r <= 2 | 9.56 17.85 19.96 24.60
>r <= 1 | 29.03 32.00 34.91 41.07
>r = 0 | 62.64 49.65 53.12 60.16
>which indicates that there is one cointegrating vector.
>Then estimated the OLS regressions of the VECM to identify the
>significant
>vector (variables) and the result looks like:
>Response E.d :
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>E.dl1 0.035197 0.243545 0.145 0.8865
>PUTEP1.dl1 0.006782 0.274279 0.025 0.9805
>PEPCC.dl1 -0.281715 0.273295 -1.031 0.3144
>Exr.dl1 0.005339 0.146832 0.036 0.9713
>E.l1 -0.709115 0.309944 -2.288 0.0326 *
>PUTEP1.l1 -0.185750 0.172672 -1.076 0.2942
>PEPCC.l1 0.583796 0.381307 1.531 0.1407
>Exr.l1 -0.157639 0.186751 -0.844 0.4081
>constant 5.922444 2.997794 1.976 0.0615 .
>---
>Multiple R-Squared: 0.32, Adjusted R-squared: 0.02863
>F-statistic: 1.098 on 9 and 21 DF, p-value: 0.4051
>
>Response PUTEP1.d :
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>E.dl1 -0.2689 0.2637 -1.020 0.319
>PUTEP1.dl1 0.1924 0.2970 0.648 0.524
>PEPCC.dl1 0.1488 0.2959 0.503 0.620
>Exr.dl1 -0.1387 0.1590 -0.872 0.393
>E.l1 0.3942 0.3356 1.175 0.253
>PUTEP1.l1 0.2514 0.1870 1.345 0.193
>PEPCC.l1 -0.5425 0.4128 -1.314 0.203
>Exr.l1 0.2921 0.2022 1.445 0.163
>constant -4.2368 3.2457 -1.305 0.206
>Residual standard error: 0.1083 on 21 degrees of freedom
>Multiple R-Squared: 0.4095, Adjusted R-squared: 0.1564
>F-statistic: 1.618 on 9 and 21 DF, p-value: 0.1740
>
>Response PEPCC.d :
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>E.dl1 0.04139 0.21105 0.196 0.8464
>PUTEP1.dl1 0.36818 0.23768 1.549 0.1363
>PEPCC.dl1 -0.03719 0.23683 -0.157 0.8767
>Exr.dl1 0.11927 0.12724 0.937 0.3592
>E.l1 0.18207 0.26859 0.678 0.5053
>PUTEP1.l1 0.36989 0.14963 2.472 0.0221 *
>PEPCC.l1 -0.80442 0.33043 -2.435 0.0239 *
>Exr.l1 -0.01621 0.16183 -0.100 0.9212
>constant -1.19117 2.59777 -0.459 0.6513
>---
>Residual standard error: 0.08666 on 21 degrees of freedom
>Multiple R-Squared: 0.581, Adjusted R-squared: 0.4014
>F-statistic: 3.235 on 9 and 21 DF, p-value: 0.01275
>
>Response Exr.d :
>Coefficients:
> Estimate Std. Error t value Pr(>|t|)
>E.dl1 0.22674 0.25078 0.904 0.37617
>PUTEP1.dl1 0.70895 0.28243 2.510 0.02032 *
>PEPCC.dl1 -0.03344 0.28141 -0.119 0.90653
>Exr.dl1 0.27850 0.15119 1.842 0.07964 .
>E.l1 -0.70257 0.31915 -2.201 0.03903 *
>PUTEP1.l1 -0.40521 0.17780 -2.279 0.03323 *
>PEPCC.l1 0.74434 0.39263 1.896 0.07184 .
>Exr.l1 -0.93802 0.19230 -4.878 8e-05 ***
>constant 9.64131 3.08684 3.123 0.00514 **
>---
>Residual standard error: 0.103 on 21 degrees of freedom
>Multiple R-Squared: 0.6468, Adjusted R-squared: 0.4955
>F-statistic: 4.274 on 9 and 21 DF, p-value: 0.002914
>I also performed the Granger causality test using
>granger.test() function
>and the result looks like:
> F-statistic p-value
>dPUTEP1 -> dE 0.2652173 0.6107489208
>dPEPCC -> dE 0.3099271 0.5823104521
>dExr -> dE 0.0756436 0.7853839986
>dE -> dPUTEP1 0.2927093 0.5929257035
>dPEPCC -> dPUTEP1 0.9240658 0.3449401105
>dExr -> dPUTEP1 0.5893134 0.4493465819
>dE -> dPEPCC 1.2787679 0.2680733692
>dPUTEP1 -> dPEPCC 16.4966125 0.0003759451
>dExr -> dPEPCC 0.0877026 0.7693843210
>dE -> dExr 0.7935924 0.3808859838
>dPUTEP1 -> dExr 1.8548683 0.1844741419
>dPEPCC -> dExr 2.5682890 0.1206617216
>The granger causality test shows that dPUTEP1 causes dPEPCC
>but in addition
>to that the OLS of the VECM shows that PUTEP1 and E.l1 also
>causes dExr.
>Given that there is only one cointegrating vector, which way
>is the right
>way to identify that cointegrating vector? Do I have to use
>the OLS of the
>VECM? If so, the OLS is showing more than one cointegrating
>vector. that was
>my confusion. Any help is highly appreciated.
>Thanks,
>Bereket
>
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