> # Null hypothesis:

> # There are n cointegrated vectors.

有n个协整向量

> install.packages('urca')

> library(urca)

> args(ca.jo)

function (x, type = c('eigen', 'trace'), ecdet = c('none', 'const',

'trend'), K = 2, spec = c('longrun', 'transitory'), season = NULL,

dumvar = NULL)

NULL

> # x: data matrix to be investigated for cointegration

x: 用于检查协整的数据矩阵

> # type: 'eigen' or 'trace'

> # ecdet: 'none', 'const', or 'trend'

> # K: number of lags

K: 滞后阶数

> # spec: VECM specification, 'longrun' or 'transitory'

spec: VECM规范：'longrun'或'transitory'

> # Example:

> data(denmark)

> sjd ->

> (sjd.vecm ->

+ spec='longrun',season=4))

#################################

# Johansen-Procedure Unit Root / Cointegration Test #

#################################

The value of the test statistic is: 2.3522 6.3427 10.362 30.0875

> summary(sjd.vecm)

######################

# Johansen-Procedure #

######################

Test type: maximal eigenvalue statistic (lambda max) , without linear trend and constant in cointegration

测试类型：没有线性趋势并协整恒定的最大特征值统计(λ最大)

Eigenvalues (lambda):

特征值(λ)：

[1] 4.331654e-01 1.775836e-01 1.127905e-01 4.341130e-02

[5] -8.947236e-16

Values of teststatistic and critical values of test:

测试检验统计量的值和临界值：

test 10pct 5pct 1pct

r <= 3="" |="" 2.35="" 7.52="" 9.24="">=>

r <= 2="" |="" 6.34="" 13.75="" 15.67="">=>

r <= 1="" |="" 10.36="" 19.77="" 22.00="">=>

r = 0 | 30.09 25.56 28.14 33.24

Eigenvectors, normalised to first column:

归一化的特征向量

(These are the cointegration relations)

没有协整关系

LRM.l2 LRY.l2 IBO.l2 IDE.l2 constant

LRM.l2 1.000000 1.0000000 1.0000000 1.000000 1.0000000

LRY.l2 -1.032949 -1.3681031 -3.2266580 -1.883625 -0.6336946

IBO.l2 5.206919 0.2429825 0.5382847 24.399487 1.6965828

IDE.l2 -4.215879 6.8411103 -5.6473903 -14.298037 -1.8951589

constant -6.059932 -4.2708474 7.8963696 -2.263224 -8.0330127

Weights W:

(This is the loading matrix)

(这是载荷矩阵)

LRM.l2 LRY.l2 IBO.l2 IDE.l2

LRM.d -0.21295494 -0.00481498 0.035011128 2.028908e-03

LRY.d 0.11502204 0.01975028 0.049938460 1.108654e-03

IBO.d 0.02317724 -0.01059605 0.003480357 -1.573742e-03

IDE.d 0.02941109 -0.03022917 -0.002811506 -4.767627e-05

constant

LRM.d -4.183363e-13

LRY.d 4.618135e-13

IBO.d 3.673136e-14

IDE.d -1.115087e-14

> slotNames(sjd.vecm)

[1] 'x' 'Z0' 'Z1' 'ZK' 'type'

[6] 'model' 'ecdet' 'lag' 'P' 'season'

[11] 'dumvar' 'cval' 'teststat' 'lambda' 'Vorg'

[16] 'V' 'W' 'PI' 'DELTA' 'GAMMA'

[21] 'R0' 'RK' 'bp' 'spec' 'call'

[26] 'test.name'

> sjd.vecm@teststat

[1] 2.352233 6.342730 10.361950 30.087451

> sjd.vecm@cval # 10.36 <><=1 =="" 22.00="">=1>

10pct 5pct 1pct

r <= 3="" |="" 7.52="" 9.24="">=>

r <= 2="" |="" 13.75="" 15.67="">=>

r <= 1="" |="" 19.77="" 22.00="">=>

r = 0 | 25.56 28.14 33.24

> # Conclusion: There are 1 cointegrated vector.

结论：有1个协整向量。