Thanks for the inputs Marc. You provide some interesting insights. Yes,
they are all prices. In my case the prices are very close to difference
stationary actually. But none the less, any particular tool that you will
recommend when it comes to testing for pairs trading. That is the ultimate
application of interest, which is why I was interested in cointegration in
the first place.


On Sat, Jun 15, 2013 at 1:54 AM, Wildi Marc (wlmr) <wlmr@zhaw.ch> wrote:

> Ganesha, Brian, All
>
> The log-return transformation typically eliminates trends of `prices' (the
> latter should behave not too far away from a random-walk although we all
> know that's not entirely true because otherwise this Mailing list wouldn't
> exist).  Therefore the empirical significance Level of the ADF-test should
> be markedly below 5% for log-Returns (except if there is/are shift(s) in
> the transformed data!). The posted results (25%) strongly suggest Prices
> (not log-Returns).
>
> Cointegration: this is an econometrician tool developped for `stable'
> (difference-stationary Gaussian) series which `behave well' over longer
> time spans: Forget about application of this very sensitive stuff to
> non-stationary financial data. Prices are not difference-stationary!
> Econometrician are interested in the DGP (data generating process), not in
> generating trading performances: therefore typical optimization criteria
> are misleading: all statistics address one-step ahead mean-square
> performances; who in the world (besides econometrician) is interested in
> such a criterion?
>
> My advice: skip this unreliable Topic and save some time for leisure!
>
> Marc
>
> ________________________________________
> Von: r-sig-finance-bounces@r-project.org [
> r-sig-finance-bounces@r-project.org]&quot; im Auftrag von &quot;Brian G.
> Peterson [brian@braverock.com]
> Gesendet: Freitag, 14. Juni 2013 18:14
> An: r-sig-finance@r-project.org
> Betreff: Re: [R-SIG-Finance] Cointegration question.
>
> Please don't repost.  If someone has the answer to your question and
> feels like helping, they will.
>
> The most common problem we see in the list archives when questions like
> this arise is that people are trying to test stationarity and
> cointegration on prices rather than on returns.
>
> However, you haven't actually provided reproducible data with your
> partial code, so without that I'm just guessing.
>
>   - Brian
>
> On 06/14/2013 11:09 AM, ganesha0701 wrote:
> > I have two time series that I am investigating, acc and amb, the time
> > frequency is daily data. They are both non stationary, as evidenced by
> the
> > follows.
> >
> >
> >
> > adf.test(df$acc)
> >
> >          Augmented Dickey-Fuller Test
> >
> > data:  df$acc
> > Dickey-Fuller = -2.7741, Lag order = 5, p-value = 0.2519
> > alternative hypothesis: stationary
> >
> >> adf.test(df$amb)
> >
> >          Augmented Dickey-Fuller Test
> >
> > data:  df$amb
> > Dickey-Fuller = -1.9339, Lag order = 5, p-value = 0.6038
> > alternative hypothesis: stationary
> >
> > I am looking to test for cointegration between the two time series but
> the
> > problem I am running into is that the cointegrating vector seems to
> change
> > in time.
> >
> >
> > 1)* First 200 points*
> >
> > ######################
> > # Johansen-Procedure #
> > ######################
> >
> > Test type: maximal eigenvalue statistic (lambda max) , with linear trend
> >
> > Eigenvalues (lambda):
> > [1] 0.0501585398 0.0003129906
> >
> > Values of teststatistic and critical values of test:
> >
> >            test 10pct  5pct  1pct
> > r <= 1 |  0.06  6.50  8.18 11.65
> > r = 0  | 10.19 12.91 14.90 19.19
> >
> > Eigenvectors, normalised to first column:
> > (These are the cointegration relations)
> >
> >             acc.l2    amb.l2
> > acc.l2  1.0000000  1.000000
> > amb.l2 -0.9610573 -2.237141
> >
> > Weights W:
> > (This is the loading matrix)
> >
> >             acc.l2       amb.l2
> > acc.d -0.03332428 -0.002576070
> > amb.d  0.03986111 -0.001591227
> >
> >
> > 2) *First 1000 points*
> >
> > ######################
> > # Johansen-Procedure #
> > ######################
> >
> > Test type: maximal eigenvalue statistic (lambda max) , with linear trend
> >
> > Eigenvalues (lambda):
> > [1] 0.019211132 0.001959403
> >
> > Values of teststatistic and critical values of test:
> >
> >            test 10pct  5pct  1pct
> > r <= 1 |  1.96  6.50  8.18 11.65
> > r = 0  | 19.36 12.91 14.90 19.19
> >
> > Eigenvectors, normalised to first column:
> > (These are the cointegration relations)
> >
> >             acc.l2   amb.l2
> > acc.l2  1.0000000  1.00000
> > amb.l2 -0.8611314 15.76683
> >
> > Weights W:
> > (This is the loading matrix)
> >
> >              acc.l2        amb.l2
> > acc.d -0.008993595 -0.0002419353
> > amb.d  0.027935684 -0.0002067523
> >
> >
> > 3)* Whole History*
> >
> > ######################
> > # Johansen-Procedure #
> > ######################
> >
> > Test type: maximal eigenvalue statistic (lambda max) , with linear trend
> >
> > Eigenvalues (lambda):
> > [1] 0.0144066813 0.0008146258
> >
> > Values of teststatistic and critical values of test:
> >
> >            test 10pct  5pct  1pct
> > r <= 1 |  1.16  6.50  8.18 11.65
> > r = 0  | 20.64 12.91 14.90 19.19
> >
> > Eigenvectors, normalised to first column:
> > (These are the cointegration relations)
> >
> >             acc.l2    amb.l2
> > acc.l2  1.0000000   1.00000
> > amb.l2 -0.8051537 -25.42806
> >
> > Weights W:
> > (This is the loading matrix)
> >
> >             acc.l2       amb.l2
> > acc.d -0.01003068 7.009487e-05
> > amb.d  0.02128464 6.980209e-05
> >
> > You can see the marginal change the coefficient values, from -0.96 to
> -0.86
> > to -0.80.
> >
> > My question is how to interpret this, what is the optimal look back
> period,
> > what is the true relationship I should use for future prediction?
> >
>
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