[R-SIG-Finance] Cointegration question.

[Brian G. Peterson]

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?
>