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

Mon Jan 12 06:45:54 CET 2009

  but why restrict A to be zero. the point is to see whether the 
regression residuals are stationary ( this determines whether the two 
series
are cointegrated.  also, did you test that they both have a unit root 
first ? ). if non zero estimate of the intercept makes the residuals  be 
more stationary from a hypothesis testing standpoint, then you may as 
well include A in the initial regresssion. I say that partally based
on intuition in that if the intercept really is zero, A should get 
estimated near zero but it's also based on guess work.

on the other hand,  testing whether  any series has a unit root ( the 
dickey fuller stuff ) is where inclusion or not of the intercept gets 
very tricky. hamilton has a very nice chapter on that. i think 17. i'm 
pretty sure though that including the intercept in the cointegrating 
regression itself  can't hurt you. maybe someone can confirm or 
unconfirm this ? it's been a while since I looked at this material.

On Sun, Jan 11, 2009 at 11:18 PM, Bogaso wrote:

> I feel whether the form Y = a + bX will be taken or zero-intercept 
> form will
> be taken should be entirely based on economic theory, not from a 
> regression
> analysis. Because, in this case, as both series are non-stationary, it 
> is
> not legitimate to infer anything on the coef.
>
>
>
> Bogaso wrote:
>>
>> 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
>>>>>
>>>>> _______________________________________________
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>>
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