[R-SIG-Finance] cointegration using Johansen for VAR

[Pfaff, Bernhard Dr.]

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: r-sig-finance-bounces at r-project.org 
> [mailto:r-sig-finance-bounces at r-project.org] Im Auftrag von algotr8der
> Gesendet: Dienstag, 26. April 2011 04:30
> An: r-sig-finance at r-project.org
> 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.
> 
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