
Hi,
 
Suppose Y and X are cointegrated. The cointegration regression can be written as
 
Y = a + bX.
 
Setting a = 0 means that you are forcing the line between Y and X to go thru the origin. 
If the true value of a is in fact 0, this is innocuos. If not (which is the case in general), it can distort the estimated value for b.
 
So it is better to consider non-zero intercept, unless you are sure that a is truly 0.
Hope this help. > Date: Sun, 11 Jan 2009 17:25:00 -0800> From: bogaso.christofer@gmail.com> To: r-sig-finance@stat.math.ethz.ch> Subject: Re: [R-SIG-Finance] [R-sig-finance] Fw: Testing for cointegration: Johansen vs Dickey-Fuller> > > I have one question. What is the point to keep constant in cointegration> euqation? I think you should consider zero intercept in cointegrating> equation.> > > > Jae Kim-3 wrote:> > > > From: "Jae Kim" <jh8080@hotmail.com>> > Sent: Saturday, January 10, 2009 10:04 AM> > To: "Paul Teetor" <paulteetor@yahoo.com>> > Subject: Re: [R-SIG-Finance] Testing for cointegration: Johansen vs > > Dickey-Fuller> > > >> Hi,> >>> >> 1. If you are using the ADF test here, you are giving the restriction> >> that > >> the cointegrating vector between the two is (1, -1.2534). That is, you > >> are saying that the two variables are related in the long run with the > >> cointegrating vector given. Under this restriction, you find the spread > >> stationary, so they are cointegrated with given cointegrating vector.> >>> >> 2. If you are using Johansen method, you are doing unrestricted> >> estimation > >> of cointegrating vector. But if you believe that the above restriction is > >> sensible economically, the ADF result should be preferred to Johansen > >> result.> >>> >> 3. This is the bivariate case, so Johansen method may not be necessary. > >> try Engle-Granger 2-stage method, you might find cointegration. In > >> addition, Johansen method assumes normality, which may often be violated.> >>> >> hope this helps. JHK> >>> >>> >> --------------------------------------------------> >> From: "Paul Teetor" <paulteetor@yahoo.com>> >> Sent: Saturday, January 10, 2009 8:38 AM> >> To: <r-sig-finance@stat.math.ethz.ch>> >> Subject: [R-SIG-Finance] Testing for cointegration: Johansen vs > >> Dickey-Fuller> >>> >>> R SIG Finance readers:> >>>> >>> I am checking a futures spread for mean reversion. I am using the > >>> Johansen> >>> test (ca.jo) for cointegration and the Augmented Dickey-Fuller test > >>> (ur.df)> >>> for mean reversion.> >>>> >>> Here is the odd part: The Johansen test says the two futures prices are > >>> not> >>> cointegrated, but the ADF test says the spread is, in fact, > >>> mean-reverting.> >>>> >>> I am very puzzled. The spread is a linear combination of the prices,> >>> and> >>> the ADF test says it is mean-reverting. But the failed Johansen test > >>> says> >>> the prices are not cointegrated, so no linear combination of prices is> >>> mean-reverting. Huh??> >>>> >>> I would be very grateful is someone could suggest where I went wrong, or> >>> steer me towards some relevent reference materials.> >>>> >>>> >>> Background: I am studying the spread between TY futures (10-year US> >>> Treasurys) and SR futures (10-year US swap rate), calculated as:> >>>> >>> sprd = ty - (1.2534 * sr)> >>>> >>> where ty and sr are the time series of futures prices. (The 1.2534 > >>> factor> >>> is from an ordinary least squares fit.) I execute the Johansen> >>> procedure> >>> this way:> >>>> >>> ca.jo(data.frame(ty, sr), type="eigen", ecdet="const")> >>>> >>> The summary of the test result is:> >>>> >>> ######################> >>> # Johansen-Procedure #> >>> ######################> >>>> >>> Test type: maximal eigenvalue statistic (lambda max) , without> >>> linear trend and constant in cointegration> >>>> >>> Eigenvalues (lambda):> >>> [1] 2.929702e-03 6.616599e-04 -1.001412e-17> >>>> >>> Values of teststatistic and critical values of test:> >>>> >>> test 10pct 5pct 1pct> >>> r <= 1 | 2.00 7.52 9.24 12.97> >>> r = 0 | 8.89 13.75 15.67 20.20> >>>> >>> <snip>> >>>> >>> I interpret the "r <= 1" line this way: The test statistic for r <= 1> >>> is> >>> below the critical values, hence we cannot reject the null hypothesis > >>> that> >>> the rank is less than 2. We conclude that the two time series are not> >>> cointegrated.> >>>> >>> I run the ADF test this way:> >>>> >>> ur.df(sprd, type="drift")> >>>> >>> (I set type="drift" because that seems to correspond to ecdet="const"> >>> for> >>> the Johansen test.) The summary of the ADF test is:> >>>> >>> ###############################################> >>> # Augmented Dickey-Fuller Test Unit Root Test #> >>> ###############################################> >>>> >>> Test regression drift> >>>> >>> <snip>> >>>> >>> Value of test-statistic is: -2.9624 4.4142> >>>> >>> Critical values for test statistics:> >>> 1pct 5pct 10pct> >>> tau2 -3.43 -2.86 -2.57> >>> phi1 6.43 4.59 3.78> >>>> >>> I interpret the test statistics as meaning we can reject the null > >>> hypothesis> >>> of a unit root (at a confidence level of 90% or better), hence the> >>> spread > >>> is> >>> mean-reverting. I get similar results from the adf.test() procedure.> >>>> >>> F.Y.I., I am running version 2.6.2 of R.> >>>> >>> Paul Teetor> >>> Elgin, IL USA> >>>> >>> _______________________________________________> >>> R-SIG-Finance@stat.math.ethz.ch mailing list> >>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance> >>> -- Subscriber-posting only.> >>> -- If you want to post, subscribe first.> >>>> > > > _______________________________________________> > R-SIG-Finance@stat.math.ethz.ch mailing list> > https://stat.ethz.ch/mailman/listinfo/r-sig-finance> > -- Subscriber-posting only.> > -- If you want to post, subscribe first.> > > > > > -- > View this message in context: http://www.nabble.com/Fw%3A-Testing-for-cointegration%3A-Johansen-vs-Dickey-Fuller-tp21382220p21406957.html> Sent from the Rmetrics mailing list archive at Nabble.com.> > _______________________________________________> R-SIG-Finance@stat.math.ethz.ch mailing list> https://stat.ethz.ch/mailman/listinfo/r-sig-finance> -- Subscriber-posting only.> -- If you want to post, subscribe first.
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