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Estimate VEC Model Parameters Using jcitest

In addition to testing for multiple cointegrating relations, jcitest produces maximum likelihood estimates of VEC model coefficients under the rank restrictions on B. Estimation information is returned in an optional fifth output argument, and can be displayed by setting an optional input parameter. For example, the following estimates a VEC(2) model of the data, and displays the results under each of the rank restrictions r = 0, r = 1, and r = 2:

load Data_Canada
Y = Data(:,3:end); % Interest rate data
[~,~,~,~,mles] = jcitest(Y,'model','H1','lags',2,...
    'display','params');
****************************
Parameter Estimates (Test 1)

r = 0
------
B1 =
   -0.1848    0.5704   -0.3273
    0.0305    0.3143   -0.3448
    0.0964    0.1485   -0.1406

B2 =
   -0.6046    1.6615   -1.3922
   -0.1729    0.4501   -0.4796
   -0.1631    0.5759   -0.5231

c1 =
    0.1420
    0.1517
    0.1508


r = 1
------
A =
   -0.6259
   -0.2261
   -0.0222

B =
    0.7081
    1.6282
   -2.4581

B1 =
    0.0579    1.0824   -0.8718
    0.1182    0.4993   -0.5415
    0.1050    0.1667   -0.1600

B2 =
   -0.5462    2.2436   -1.7723
   -0.1518    0.6605   -0.6169
   -0.1610    0.5966   -0.5366

c0 =
    2.2351

c1 =
   -0.0366
    0.0872
    0.1444


r = 2
------
A =
   -0.6259    0.1379
   -0.2261   -0.0480
   -0.0222    0.0137

B =
    0.7081   -2.4407
    1.6282    6.2883
   -2.4581   -3.5321

B1 =
    0.2438    0.6395   -0.6729
    0.0535    0.6533   -0.6107
    0.1234    0.1228   -0.1403

B2 =
   -0.3857    1.7970   -1.4915
   -0.2076    0.8158   -0.7146
   -0.1451    0.5524   -0.5089

c0 =
    2.0901
   -3.0289

c1 =
   -0.0104
    0.0137
    0.1528

mles is a tabular array of structure arrays, with each structure containing information for a particular test under a particular rank restriction. Since both tabular arrays and structure arrays use similar indexing, you can access the tabular array and then the structure using dot notation. For example, to access the rank 2 matrix of cointegrating relations:

B = mles.r2.paramVals.B
B = 3×2

    0.7081   -2.4407
    1.6282    6.2883
   -2.4581   -3.5321

See Also

Related Examples

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