This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

Determine Cointegration Rank of VEC Model

This example shows how to convert an n-dimensional VAR model to a VEC model, and then compute and interpret the cointegration rank of the resulting VEC model.

The rank of the error-correction coefficient matrix, C, determines the cointegration rank. If rank(C) is:

  • Zero, then the converted VEC(p) model is a stationary VAR(p - 1) model in terms of Δyt, without any cointegration relations.

  • n, then the VAR(p) model is stable in terms of yt.

  • The integer r such that 0<r<n, then there are r cointegrating relations. That is, there are r linear combinations that comprise stationary series. You can factor the error-correction term into the two n-by- r matrices C=αβ. α contains the adjustment speeds, and β the cointegration matrix. This factorization is not unique.

For more details, see Cointegration and Error Correction and [80], Chapter 6.3.

Consider the following VAR(2) model.

yt=[10.260-0.110.350.12-0.051.15]yt-1+[-0.2-0.1-0.10.6-0.4-0.1-0.02-0.03-0.1]yt-2+εt.

Create the variables A1 and A2 for the autoregressive coefficients. Pack the matrices into a cell vector.

A1 = [1 0.26 0; -0.1 1 0.35; 0.12 -0.5 1.15];
A2 = [-0.2 -0.1 -0.1; 0.6 -0.4 -0.1; -0.02 -0.03 -0.1];
Var = {A1 A2};

Compute the autoregressive and error-correction coefficient matrices of the equivalent VEC model.

[Vec,C] = var2vec(Var);

Because the degree of the VAR model is 2, the resulting VEC model has degree q=2-1. Hence, Vec is a one-dimensional cell array containing the autoregressive coefficient matrix.

Determine the cointegration rank by computing the rank of the error-correction coefficient matrix C.

r = rank(C)
r = 2

The cointegrating rank is 2. This result suggests that there are two independent linear combinations of the three variables that are stationary.

See Also

|

Related Examples

More About