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I'm relatively new to the VAR model and have been using Sean Becketti's 'Introduction to Time Series Using State' as reference and wanted to check if I am on the right track.

As of now, I have 5 variables in the VAR Model. [GDP, Oil prices, Exchanged rates (Expressed in Logs)] , [Inflation Rate and Unemployment Rate (Expressed in percentages)]

I performed the Unit Root tests and all of them proved to be non-stationary and did the Johansen Cointegration tests using

vecrank lrgdp lop lexc inf unp, max ic

The results show that the variables do not have any cointegrating relationships. However, the variables contain a unit root, I don't know if I should estimate the VAR using the variables in their first differences or in levels. I did it in levels

varbasic lrgdp lop lexc inf unp, lags (1 2 3 4 5)

but I'm not sure if it should be that or

varbasic dlrgdp dlop dlexc dinf dunp, lags (1 2 3 4 5)

These are my variables

Code:

Example generated by -dataex-. To install: ssc install dataex
clear
input float(lrgdp lop lexc) double(unp inf) float(Dlrgdp Dlop Dlexc Dunp Dinf)
12.733817  3.571784  1.598734              1.5  7.74278215223094            .            .            .           .           .
12.690648  3.568123 1.5978713              1.4  10.2464332036316   -.04316902 -.0036604404 -.0008628368         -.1    2.503651
12.661692  3.487579 1.5771695              2.1   12.291933418694  -.028956413   -.08054447  -.020701766          .7   2.0455003
12.745687 3.6658666  1.614704              1.6  13.1147540983606    .08399487    .17828774    .03753448         -.5    .8228207
12.734313 3.6188145 1.6771152              1.8  14.7381242387332   -.01137352   -.04705215    .06241119          .2     1.62337
  12.7117  3.512739 1.7375907                2                14  -.022613525   -.10607576    .06047547          .2   -.7381243
12.695962 3.4593616  1.805854              2.4  13.5689851767389  -.015737534   -.05337715    .06826341          .4   -.4310148
12.754564 3.5122416 1.7645824              1.8  12.3745819397994    .05860233    .05288005   -.04127169         -.6  -1.1944033
12.734605  3.423394 1.7836152                2  11.8895966029724   -.01995945   -.08884788   .019032836          .2  -.48498535
 12.70936  3.469064 1.8045276              2.4  11.0423116615067  -.025244713    .04567003    .02091241          .4   -.8472849
12.699594  3.459676  1.893353              2.8  10.8433734939759  -.009765625  -.009387732    .08882523          .4  -.19893816
12.762194 3.4528406 1.9665668              3.2  11.6071428571428    .06259918   -.00683546   .073213935          .4    .7637694
12.752794  3.372798  1.961493              3.6  9.77229601518024  -.009399414    -.0800426  -.005073905          .4   -1.834847
12.759803  3.383712 1.9698684              3.7   9.1078066914498   .007008553   .010914087  .0083755255          .1   -.6644893
 12.74189  3.411038 2.0019078              3.8  7.78985507246374  -.017912865    .02732563   .032039404          .1  -1.3179516
12.807036  3.365225  2.015254              2.6  7.28888888888891   .065146446   -.04581285   .013346195        -1.2   -.5009662
 12.81646   3.37531 2.0397863              3.2  6.30942091616251    .00942421   .010084867    .02453232          .6    -.979468
12.796157 3.3780425 2.0465481              3.3  6.47359454855195  -.020303726   .002732754    .00676179          .1   .16417363
12.817017  3.337429 2.1241918              3.6  6.13445378151261    .02085972   -.04061341    .07764363          .3   -.3391408
12.866818  3.313822 2.1803722              2.5  5.96520298260146    .04980183  -.023606777    .05618048        -1.1   -.1692508
12.878362  3.309326  2.237168                3  5.69105691056911   .011543274 -.0044965744    .05679584          .5  -.27414608
 12.84228  3.293983 2.1853395              2.3  5.75999999999999  -.036082268  -.015342474   -.05182862         -.7   .06894309
12.861259  3.299288  2.121343              3.1  5.77988915281077    .01897907   .005304575   -.06399655          .8  .019889154
12.929962   3.33482 2.0523486                2  5.62939796716187    .06870365   .035532236   -.06899428        -1.1   -.1504912
12.903667  2.842581 1.9905694                2  5.76923076923076   -.02629471     -.492239   -.06177926           0    .1398328
12.897962  2.521185  2.001881              1.9  6.05143721633889  -.005705833    -.3213961    .01131153         -.1   .28220645
 12.89723  2.521185 1.9996946              2.3  8.00898203592812 -.0007314682            0 -.0021862984          .4   1.9575448
12.971673 2.6837575  2.010828              1.7  8.80829015544041    .07444286     .1625726   .011133432         -.6    .7993081
 12.92926  2.873941  1.950964              2.4  9.96363636363637   -.04241371    .19018364   -.05986404          .7   1.1553462
12.932686  2.911807 1.9037777              1.8  9.70042796005709   .003426552    .03786588   -.04718626         -.6   -.2632084
12.893644  2.941276  1.906605              2.2  7.90020790020794   -.03904152   .029469013  .0028271675          .4    -1.80022
12.984353  2.876761 1.8676294              1.9  7.41496598639454    .09070873  -.064515114   -.03897548         -.3   -.4852419
12.946301  2.757052 1.8508142              2.5  7.07671957671957    -.0380516   -.11970901  -.016815186          .6   -.3382464
12.911412  2.778198  1.833541              2.9  7.02210663198959   -.03488922    .02114606  -.017273188          .4  -.05461295
 12.90235 2.6452286  1.922188              3.4  6.61528580603723  -.009062767   -.13296938    .08864713          .5   -.4068208
12.970265  2.576168   1.88874              3.9  6.01646611779607    .06791592  -.069060326   -.03344822          .5   -.5988197
12.919985  2.834585 1.9055742              4.8  4.69425571340333   -.05028057    .25841665   .016834259          .9  -1.3222104
 12.94254  2.916148  1.947119 4.76666666666667  4.67800729040098    .02255535    .08156276     .0415448 -.033333335 -.016248424
12.918333  2.857045  1.951395 5.03333333333333  4.51807228915663  -.024207115   -.05910301   .004276037   .26666668    -.159935
 12.99056 2.9295924 1.9239225 4.93333333333333  4.30107526881723    .07222748   .072547674  -.027472496         -.1  -.21699703
12.966217  2.968532  1.876953 5.66666666666667  4.36578171091446   -.02434349    .03893995   -.04696953    .7333333  .064706445
12.940326  2.761275 1.8701546 5.16666666666667  3.83052814857803  -.025891304   -.20725727  -.006798387         -.5   -.5352536
12.928958 3.2448034 1.8171023              5.2  3.80403458213255  -.011367798     .4835284   -.05305231  .033333335 -.026493566
 13.01213  3.433987  1.768508 4.83333333333333    4.524627720504     .0831728     .1891837   -.04859436   -.3666667    .7205932
12.980206  2.988204 1.7871656              5.6  3.90050876201245    -.0319252    -.4457831   .018657684    .7666667    -.624119
12.994061  2.908539  1.910165 5.23333333333333  3.80100614868644   .013855934   -.07966495    .12299943   -.3666667  -.09950262
12.965244  2.966475 1.9188864 5.46666666666667  3.49805663520268  -.028817177    .05793595   .008721352   .23333333   -.3029495
 13.03053  2.989043 1.8550003              5.5  2.57534246575342    .06528664   .022568226  -.063886166  .033333335   -.9227142
 13.03316  2.862582 1.8492314              6.1  2.33949945593033    .00262928    -.1264615  -.005768895          .6    -.235843
13.002828  2.979772 1.8425794 5.96666666666667   2.4232633279483  -.030332565     .1171906  -.006651998  -.13333334   .08376388
13.011215  2.995566 1.7568114                6  2.30686695278971   .008387566   .015793324   -.08576798  .033333335  -.11639638
13.063393 2.9421556 1.8557254 5.63333333333333  2.24358974358973    .05217743   -.05341005    .09891403   -.3666667  -.06327721
 13.03319  2.889816 1.9392883 6.26666666666667  2.60499734183944   -.03020191   -.05233955    .08356285    .6333333    .3614076
13.020434  2.890001 1.9237765              6.1  2.41850683491062  -.012756348 .00018525124   -.01551175  -.16666667   -.1864905
13.036485  2.785011  1.981176              6.1  2.14997378080752   .016050339      -.10499    .05739963           0  -.26853305
13.129934  2.705603   1.99125 5.33333333333333  1.98537095088822     .0934496   -.07940865    .01007378   -.7666667  -.16460283
13.086267  2.629728 2.0071983 5.63333333333333   1.2435233160622   -.04366684   -.07587433   .015948415          .3   -.7418476
13.094742  2.789323   1.97535 5.66666666666667  .975359342915802    .00847435    .15959454  -.031848192  .033333335  -.26816398
13.069872   2.83615   1.92342 5.36666666666667  1.54004106776183   -.02486992    .04682732   -.05193007         -.3    .5646817
13.167482 2.8096035  1.907233 4.96666666666667  1.74180327868853    .09761047  -.026546717  -.016186953         -.4    .2017622
13.138304  2.846265 1.8751172 5.53333333333333  2.66120777891503   -.02917862   .036661625  -.032115936   .56666666    .9194045
13.106668 2.9001386 1.8304694              5.2  2.69445856634468  -.031635284    .05387354   -.04464781   -.3333333  .033250786
 13.13269 2.7997174 1.8410743              4.8   2.3255813953488    .02602291    -.1004212   .010604978         -.4   -.3688772
13.203746   2.83184 1.8371985              4.2  2.16515609264855    .07105446   .032122374 -.0038758516         -.6   -.1604253
13.192417 2.9076295 1.8587487                5  .897308075772663  -.011328697     .0757897    .02155018          .8   -1.267848
13.162365 2.9697304 1.8772483                5  .990099009900991  -.030052185    .06210089   .018499613           0   .09279093
13.191945  3.026746 1.8584784 4.76666666666667  1.38339920948619   .029580116     .0570159   -.01876986  -.23333333    .3933002
13.232254  3.138244 1.8616062 4.23333333333333  1.77427304090683    .04030895    .11149788   .003127813  -.53333336    .3908738
13.214523  3.048483 1.8915474 4.26666666666667  3.06324110671939  -.017730713   -.08976126     .0299412  .033333335    1.288968
13.248065   2.91723 1.9568384 4.23333333333333  2.69607843137256    .03354168   -.13125277    .06529093 -.033333335   -.3671627
13.222542 2.9262035 2.0096192 3.96666666666667  2.29044834307992  -.025523186    .00897336    .05278087  -.26666668   -.4056301
 13.29889  2.935982  1.963833              3.2  2.22760290556901     .0763483   .009778738   -.04578638   -.7666667  -.06284544
13.286092 2.6506565 2.0201964              3.3  2.15723873441995   -.01279831   -.28532577    .05636358          .1  -.07036417
13.259114  2.586259 2.0167592 3.46666666666667   2.2434367541766   -.02697754  -.064397335  -.003437281   .16666667   .08619802
 13.23906  2.565206 2.0330641              3.1  2.28680323963794   -.02005291  -.021053314    .01630497   -.3666667   .04336648
 13.30432  2.472328 2.0134616              2.5  2.32117479867363    .06525898   -.09287786  -.019602537         -.6   .03437156
13.283984  2.454734 2.0364158              2.8  2.25246363209761   -.02033615  -.017594099   .022954226          .3  -.06871117
 13.26049  2.774462 2.0538929 2.96666666666667  2.47432306255837  -.023492813     .3197281   .017477036   .16666667   .22185943
13.274122  3.017657 2.0596468              3.2  2.04937121564973   .013630867     .2431948   .005753994   .23333333  -.42495185
 13.34865  3.169966  2.065874 3.16666666666667  2.68518518518515    .07452679    .15230894   .006227255 -.033333335     .635814
13.348047 3.2815375 2.1065755              3.4  2.89123451124368 -.0006017685    .11157179    .04070139   .23333333   .20604932
13.287727  3.287157 2.1722455              3.2  2.91571753986331    -.0603199   .005619764    .06567001         -.2   .02448303
13.296283  3.397301 2.1921618 3.33333333333333  3.42309447740759   .008555412    .11014366   .019916296   .13333334    .5073769
13.361666 3.3901365 2.2251422 3.03333333333333  3.11091073038775    .06538296  -.007164478   .032980442         -.3   -.3121837
 13.35588  3.260785 2.1848927 3.33333333333333  3.52363960749332  -.005785942   -.12935114   -.04024959          .3    .4127289
13.310266  3.285662  2.216909 3.36666666666667  3.93979637007527   -.04561424   .024876595   .032016277  .033333335    .4161568
13.320636  3.227373   2.19689 3.56666666666667   2.5595763459841   .010370255   -.05828905  -.020018816          .2    -1.38022
 13.38958 2.9607956 2.1861658 3.36666666666667   2.0113686051596    .06894302   -.26657724  -.010724306         -.2  -.54820776
 13.34324  3.040865 2.1871219 3.73333333333333   1.0340370529944   -.04633999     .0800693  .0009560585    .3666667   -.9773316
13.364398  3.226976 2.1021235 3.73333333333333  .468483816013621    .02115917     .1861112   -.08499837           0  -.56555325
13.324635 3.2934885 2.0180607 3.66666666666667  1.41996557659209   -.03976345   .066512346   -.08406281  -.06666667    .9514818
 13.40151  3.286036 1.9903824 3.53333333333333  2.22888984140592    .07687569  -.007452488   -.02767825  -.13333334    .8089243
13.380116  3.444789 1.9540068 3.96666666666667  4.60554371002131   -.02139473     .1587529   -.03637564    .4333333    2.376654
 13.33437 3.2766414 1.9471028 4.33333333333333  2.24671470962272   -.04574585   -.16814756  -.006904006    .3666667   -2.358829
 13.34543  3.345802 1.9928846 4.43333333333333  1.90920661858297   .011060715     .0691607    .04578185          .1   -.3375081
13.410333  3.379633 1.9342626              4.1  1.21593291404613   .064902306    .03383112     -.058622   -.3333333   -.6932737
13.425058   3.46979  1.932487 4.13333333333333 -1.42682429677945   .014725685    .09015703  -.001775503  .033333335   -2.642757
13.385754 3.5730944 1.9257075 4.33333333333333  .829187396351576   -.03930473    .10330415  -.006779671          .2   2.2560117
13.367247  3.702618 1.9261932              4.5  1.20732722731057  -.018507004    .12952352 .00048577785   .16666667    .3781398
13.447302  3.754901 1.8458267 4.13333333333333  1.24275062137531    .08005524    .05228329    -.0803665   -.3666667  .035423394
end
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  • $\begingroup$ VAR in levels may result in spurious regressions because your series are not stationary. You'll want to difference your series and use the VAR in differences. I am assuming differencing once gets you to stationary series. You may have to difference more than once to get stationary series. Each series entering each of your VAR regressions should be stationary otherwise you risk running spurious regressions. $\endgroup$ – ColorStatistics Jan 25 at 15:09

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