[R-SIG-Finance] Cointegration question.

[Wildi Marc (wlmr)]

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 at r-project.org [r-sig-finance-bounces at r-project.org]" im Auftrag von "Brian G. Peterson [brian at braverock.com]
Gesendet: Freitag, 14. Juni 2013 18:14
An: r-sig-finance at 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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