How to run Johansen test in Mathematica

Questions
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1

Hi,

Does anyone have any idea on wether it’s possible to run the Johansen Cointegration tests in Mathematica? If not, is the code available somewhere?

Xave

2

You may quickly take a look at this link:
http://www.verbeia.com/mathematica/mathecon/mathecon_index.html

3

Thanks Shenghui. I’ve tried this piece of code but it doesn’t seem to work on Mathematica 9.

4

Could you please post some results here or error message?

5

I am trying to test the cointegration between two ETFs.
-----------------------------------------------------------

ewa = FinancialData["NYSE:EWA", {{2006, 4, 4}, {2012, 4, 9}}, "Value"];
ewc = FinancialData["NYSE:EWC", {{2006, 4, 4}, {2012, 4, 9}}, "Value"];
data = Transpose@{ewa, ewc};

johansenProcedure[levels_?MatrixQ, p_Integer] /;
(Dimensions[levels][[ 1]] > (Dimensions[levels][[2]] + p)) :=
With[{N = Dimensions[levels][[1]], T = Dimensions[levels][[2]],
diff = Rest[levels - RotateLeft[levels]], ypt = Drop[levels, -p]},
Module[{x, r0t, rpt, s00, sop, cc, \[Lambda], v\[Lambda], log\[Lambda]},
x = Join @@ (Drop[RotateLeft[diff, #], p - 1] & /@ Range[p]);
With[{q = Inverse[Transpose[x].x], y0t = Drop[diff, p - 1]},
r0t = y0t - x.q.Transpose[x].y0t; rpt = ypt - x.q.Transpose[x].ypt; s00 = (Transpose[r0t].r0t)/T; s0p = (Transpose[r0t].rpt)/T;
cc = Inverse[CholeskyDecomposition[(Transpose[rpt].rpt)/T]];
{\[Lambda], v\[Lambda]} = Eigensystem[(cc.Transpose[s0p].Inverse[s00].s0p.Transpose[cc])];
log\[Lambda] = Log[1 - \[Lambda]];
{Reverse[-T* FoldList[Plus, First[log\[Lambda]], Rest[log\[Lambda]]]],
Reverse[-T log\[Lambda]], Join[Reverse[Transpose[Transpose[cc].v\[Lambda]]], s00, s0p]} ]]];

johansenProcedure[data, 10]

and then it keeps running until I abort

Dot::dotsh: Tensors {<<1>>} and {{0.38,0.42},{-0.21,-0.27},{0.03,0.13},{0.,-0.03},<<44>>,{0.04,0.02},{-0.56,-0.63},<<1455>>} have incompatible shapes. >>
6

@Xavier,

Usually if you have error message from your function, the best way to debug is to break a block of codes into separated cells. In your case, I notice this line is broken:

r0t = y0t - x.q.Transpose[x].y0t; 
rpt = ypt - x.q.Transpose[x].ypt;

The dimensional mismatch is from here.

7

thanks. Found the problem and it seems to work now.

8

If you got it to work, could you uplode the working code?

9

I’m the owner of the website Shenghui linked to. If there are any changes needed to be made to that code, please let me know at the email address on the web site. It is more than ten years since I posted that code and I have not had time to check which of those notebooks still work in version 9. I think I was using version 3 or 4 when I posted all that code. And as I said under the link to that notebook: "I translated the algorithm from Gauss. Untested. Use at your own risk! "

10

Could you post the code after the fix?

11

As discussed over on Mathematica.SE, I have fixed the code and it is now available at: http://www.verbeia.com/mathematica/mma/johansenprocedure.nb

12

Thank you for posting this and related discussion on MSE, Luci, it is really appreciated.