# cointegration using Johansen for VAR

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## cointegration using Johansen for VAR

 Hello everyone - I am trying to reconcile the methodology used by Enders to estimate a VAR and determine the cointegration vector using the Johansen framework (Enders pages 397-to-401) with the same as highlighted by Dr. Bernhard Pfaff in his book. My intent for the moment is to determine whether a cointegration vector exists among X variables and if so the value of the estimates in the cointegration vector. According to Enders - the methodology is as follows: 1) Determine order of integration of each variable. I have 4 variables that are I(1) - all are stock prices. 2) Determine optimal number of lag length to be included in the VAR. I do this via the VARselect function in the 'vars' package in R as highlighted in Dr. Pfaff's book. > infocrit <- VARselect(vardat, lag.max=20, type="const") > infocrit \$selection AIC(n)  HQ(n)  SC(n) FPE(n)     17      3      2     17 FIRST QUESTION: As you can see I have a conflict with the information criteria. How does one reconcile the conflict in terms of the number of lags to include in the VAR? Enders uses another method that estimates VARs with different lag lengths and then uses the likelihood ratio test (page 397 Enders). 3) Estimate the model and determine the rank of ∏. > H1 <- ca.jo(vardat, type='trace', ecdet='const', K=17) On a side note I also estimated the VAR by using "varestimate <- VAR(vardat, p=17, type="const")". I checked the residuals of each equation in the VAR for serial correlation and normality (the residuals were white noise). ---------- snippet of output of ca.jo()-------------           test 10pct  5pct  1pct r <= 3 |  2.20  7.52  9.24 12.97 r <= 2 |  6.63 17.85 19.96 24.60 r <= 1 | 15.47 32.00 34.91 41.07 r = 0  | 50.11 49.65 53.12 60.16 Eigenvectors, normalised to first column: (These are the cointegration relations)               V1.l17          V2.l17           V3.l17           V4.l17       constant V1.l17     1.0000000     1.0000000     1.0000000     1.0000000   1.00000000 V2.l17    -0.2041193    -1.1345264    -0.3982231    -0.4862289  -0.21197975 V3.l17    -0.2584363     2.6858123    -0.8965070    -0.7727329  -0.43277884 V4.l17    -0.5167626    -0.8169243    -0.4955091     0.5102647   0.06214863 constant  5.2281138   -65.4213338    84.4998981    28.3856062  0.05660371 SECOND QUESTION: Since I supplied K=17 lags (as per the AIC and FPE criterion) I'm not quite sure how to interpret the output of ca.jo(). Here is my understanding. Based on the trace test, I can reject the null: r=0 at the 90% critical value and accept r > 0. However, I must accept the null: r<= 1 given 15.47 is less than the critical values at all significance levels. So this means I have 1 cointegration vector and from documentation for ca.jo() I believe it is that depicted in the first column under the "These are the cointegration relations" heading. However, I am confused by the 'l17' suffix in each of the variables in the output. I know I have up to 17 lags in my VAR as per the AIC and FPE criterion but what does this actually say about the equilibrium relationship? Would I be incorrect to say that the equilibrium (cointegration equation) is the following: V1 - 0.2041193*V2 - 0.2584363*V3 - 0.5167626*V4 + 5.2281138 =  residuals I would greatly appreciate it if someone could help steer me in the right direction. Thank you.
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## Re: cointegration using Johansen for VAR

 Dear Algotrader, it is encountered quite often that IC will lead to different lag-specifications. In your case, I would opt for the SC or the HQ, i.e. a more parsimonuous specification and the values reported for the AIC and FPE look suspiciously high. Next, a VECM can be specified in different flavors and here you have used its long-run form. See ?ca.jo for a description and the arguments. Best, Bernhard > -----Ursprüngliche Nachricht----- > Von: [hidden email] > [mailto:[hidden email]] Im Auftrag von algotr8der > Gesendet: Dienstag, 26. April 2011 04:30 > An: [hidden email] > Betreff: [R-SIG-Finance] cointegration using Johansen for VAR > > Hello everyone - > > I am trying to reconcile the methodology used by Enders to > estimate a VAR and determine the cointegration vector using > the Johansen framework (Enders pages 397-to-401) with the > same as highlighted by Dr. Bernhard Pfaff in his book. > > My intent for the moment is to determine whether a > cointegration vector exists among X variables and if so the > value of the estimates in the cointegration vector. > > According to Enders - the methodology is as follows: > > 1) Determine order of integration of each variable. > > I have 4 variables that are I(1) - all are stock prices. > > 2) Determine optimal number of lag length to be included in the VAR. > > I do this via the VARselect function in the 'vars' package in > R as highlighted in Dr. Pfaff's book. > > > infocrit <- VARselect(vardat, lag.max=20, type="const") > > > infocrit > \$selection > AIC(n)  HQ(n)  SC(n) FPE(n) >     17      3      2     17 > > FIRST QUESTION: As you can see I have a conflict with the > information criteria. How does one reconcile the conflict in > terms of the number of lags to include in the VAR? Enders > uses another method that estimates VARs with different lag > lengths and then uses the likelihood ratio test (page 397 Enders). > > 3) Estimate the model and determine the rank of ∏. > > > H1 <- ca.jo(vardat, type='trace', ecdet='const', K=17) > > On a side note I also estimated the VAR by using "varestimate > <- VAR(vardat, p=17, type="const")". > I checked the residuals of each equation in the VAR for > serial correlation and normality (the residuals were white noise). > > ---------- snippet of output of ca.jo()------------- > >           test 10pct  5pct  1pct > r <= 3 |  2.20  7.52  9.24 12.97 > r <= 2 |  6.63 17.85 19.96 24.60 > r <= 1 | 15.47 32.00 34.91 41.07 > r = 0  | 50.11 49.65 53.12 60.16 > > Eigenvectors, normalised to first column: > (These are the cointegration relations) > >               V1.l17          V2.l17           V3.l17         >   V4.l17       > constant > V1.l17     1.0000000     1.0000000     1.0000000     > 1.0000000   1.00000000 > V2.l17    -0.2041193    -1.1345264    -0.3982231     > -0.4862289  -0.21197975 > V3.l17    -0.2584363     2.6858123    -0.8965070     > -0.7727329  -0.43277884 > V4.l17    -0.5167626    -0.8169243    -0.4955091     > 0.5102647   0.06214863 > constant  5.2281138   -65.4213338    84.4998981    28.3856062 >  0.05660371 > > > SECOND QUESTION: Since I supplied K=17 lags (as per the AIC and FPE > criterion) I'm not quite sure how to interpret the output of ca.jo(). > > Here is my understanding. Based on the trace test, I can > reject the null: > r=0 at the 90% critical value and accept r > 0. However, I > must accept the > null: r<= 1 given 15.47 is less than the critical values at > all significance levels. So this means I have 1 cointegration > vector and from documentation for ca.jo() I believe it is > that depicted in the first column under the "These are the > cointegration relations" heading. > > However, I am confused by the 'l17' suffix in each of the > variables in the output. I know I have up to 17 lags in my > VAR as per the AIC and FPE criterion but what does this > actually say about the equilibrium relationship? > > Would I be incorrect to say that the equilibrium > (cointegration equation) is the following: > > V1 - 0.2041193*V2 - 0.2584363*V3 - 0.5167626*V4 + 5.2281138 = >  residuals > > I would greatly appreciate it if someone could help steer me > in the right direction. Thank you. > > -- > View this message in context: > http://r.789695.n4.nabble.com/cointegration-using-Johansen-for> -VAR-tp3474574p3474574.html > Sent from the Rmetrics mailing list archive at Nabble.com. > > _______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only. If you want to post, subscribe first. > -- Also note that this is not the r-help list where general R > questions should go. > ***************************************************************** Confidentiality Note: The information contained in this message, and any attachments, may contain confidential and/or privileged material. It is intended solely for the person(s) or entity to which it is addressed. Any review, retransmission, dissemination, or taking of any action in reliance upon this information by persons or entities other than the intended recipient(s) is prohibited. 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