[R-SIG-Finance] cointegration using Johansen for VAR
Pfaff, Bernhard Dr.
Bernhard_Pfaff at fra.invesco.com
Tue Apr 26 15:58:27 CEST 2011
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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