# [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,

http://edoc.hu-berlin.de/series/sfb-373-papers/1999-4/PDF/4.pdf

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
>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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>
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