# [R-SIG-Finance] [R-sig-finance] Fw: Testing for cointegration: Johansen vs Dickey-Fuller

Bogaso bogaso.christofer at gmail.com
Mon Jan 12 02:25:00 CET 2009

```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 at hotmail.com>
> Sent: Saturday, January 10, 2009 10:04 AM
> To: "Paul Teetor" <paulteetor at 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 at yahoo.com>
>> Sent: Saturday, January 10, 2009 8:38 AM
>> To: <r-sig-finance at 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 at 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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