alphaols: OLS regression of VECM weighting matrix

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

This functions estimates the \bold{α} matrix of a VECM. The following OLS regression of the R-form of the VECM is hereby utilised:

\bold{R}_{0t} = \bold{α}\bold{β}\prime \bold{R}_{kt} + \bold{\varepsilon}_t \qquad t=1, …, T

Usage

1
alphaols(z, reg.number = NULL)

Arguments

z

An object of class ca.jo.

reg.number

The number of the equation in the R-form that should be estimated or if set to NULL (the default), all equations within the R-form are estimated.

Details

The cointegrating relations, i.e. \bold{R}_{kt}\prime \bold{β} are calculated by using z@RK and z@V.

Value

Returns an object of class lm.

Author(s)

Bernhard Pfaff

References

Johansen, S. (1988), Statistical Analysis of Cointegration Vectors, Journal of Economic Dynamics and Control, 12, 231–254.

Johansen, S. and Juselius, K. (1990), Maximum Likelihood Estimation and Inference on Cointegration – with Applications to the Demand for Money, Oxford Bulletin of Economics and Statistics, 52, 2, 169–210.

Johansen, S. (1991), Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica, Vol. 59, No. 6, 1551–1580.

See Also

ca.jo, lm, ca.jo-class and urca-class.

Examples

1
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data(denmark)
sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
sjd.vecm1 <- ca.jo(sjd, ecdet = "const", type="eigen", K=2, spec="longrun",
season=4)
summary(alphaols(sjd.vecm1))
summary(alphaols(sjd.vecm1, reg.number=1))

Example output

Response R0.LRM.d :

Call:
lm(formula = R0.LRM.d ~ V.RK.LRM.l2 + V.RK.LRY.l2 + V.RK.IBO.l2 + 
    V.RK.IDE.l2 + V.RK.constant - 1, data = data.mat)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039482 -0.014437 -0.005498  0.013169  0.051973 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
V.RK.LRM.l2   -2.130e-01  6.039e-02  -3.526 0.000938 ***
V.RK.LRY.l2   -4.815e-03  4.028e-02  -0.120 0.905341    
V.RK.IBO.l2    3.501e-02  2.184e-02   1.603 0.115453    
V.RK.IDE.l2    2.029e-03  2.815e-03   0.721 0.474633    
V.RK.constant -1.176e-12  3.123e-02   0.000 1.000000    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.02001 on 48 degrees of freedom
Multiple R-squared:  0.2446,	Adjusted R-squared:  0.1659 
F-statistic: 3.108 on 5 and 48 DF,  p-value: 0.01647


Response R0.LRY.d :

Call:
lm(formula = R0.LRY.d ~ V.RK.LRM.l2 + V.RK.LRY.l2 + V.RK.IBO.l2 + 
    V.RK.IDE.l2 + V.RK.constant - 1, data = data.mat)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.03448 -0.01507 -0.00100  0.01115  0.05666 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)  
V.RK.LRM.l2    1.150e-01  6.189e-02   1.859   0.0692 .
V.RK.LRY.l2    1.975e-02  4.128e-02   0.478   0.6345  
V.RK.IBO.l2    4.994e-02  2.238e-02   2.231   0.0304 *
V.RK.IDE.l2    1.109e-03  2.885e-03   0.384   0.7025  
V.RK.constant -3.424e-13  3.200e-02   0.000   1.0000  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.0205 on 48 degrees of freedom
Multiple R-squared:  0.1551,	Adjusted R-squared:  0.06707 
F-statistic: 1.762 on 5 and 48 DF,  p-value: 0.1387


Response R0.IBO.d :

Call:
lm(formula = R0.IBO.d ~ V.RK.LRM.l2 + V.RK.LRY.l2 + V.RK.IBO.l2 + 
    V.RK.IDE.l2 + V.RK.constant - 1, data = data.mat)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0232722 -0.0044453 -0.0000303  0.0048527  0.0176373 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)
V.RK.LRM.l2    2.318e-02  2.403e-02   0.965    0.340
V.RK.LRY.l2   -1.060e-02  1.602e-02  -0.661    0.512
V.RK.IBO.l2    3.480e-03  8.688e-03   0.401    0.691
V.RK.IDE.l2   -1.574e-03  1.120e-03  -1.405    0.166
V.RK.constant  2.616e-14  1.242e-02   0.000    1.000

Residual standard error: 0.00796 on 48 degrees of freedom
Multiple R-squared:  0.068,	Adjusted R-squared:  -0.02908 
F-statistic: 0.7004 on 5 and 48 DF,  p-value: 0.6258


Response R0.IDE.d :

Call:
lm(formula = R0.IDE.d ~ V.RK.LRM.l2 + V.RK.LRY.l2 + V.RK.IBO.l2 + 
    V.RK.IDE.l2 + V.RK.constant - 1, data = data.mat)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0091249 -0.0028761 -0.0000153  0.0024579  0.0148999 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)   
V.RK.LRM.l2    2.941e-02  1.524e-02   1.930  0.05949 . 
V.RK.LRY.l2   -3.023e-02  1.016e-02  -2.975  0.00458 **
V.RK.IBO.l2   -2.812e-03  5.510e-03  -0.510  0.61222   
V.RK.IDE.l2   -4.768e-05  7.104e-04  -0.067  0.94677   
V.RK.constant  1.316e-13  7.879e-03   0.000  1.00000   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.005048 on 48 degrees of freedom
Multiple R-squared:  0.211,	Adjusted R-squared:  0.1288 
F-statistic: 2.568 on 5 and 48 DF,  p-value: 0.03881



Call:
lm(formula = substitute(form1), data = data.mat)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.039482 -0.014437 -0.005498  0.013169  0.051973 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
V.RK.LRM.l2   -2.130e-01  6.039e-02  -3.526 0.000938 ***
V.RK.LRY.l2   -4.815e-03  4.028e-02  -0.120 0.905341    
V.RK.IBO.l2    3.501e-02  2.184e-02   1.603 0.115453    
V.RK.IDE.l2    2.029e-03  2.815e-03   0.721 0.474633    
V.RK.constant -1.176e-12  3.123e-02   0.000 1.000000    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.02001 on 48 degrees of freedom
Multiple R-squared:  0.2446,	Adjusted R-squared:  0.1659 
F-statistic: 3.108 on 5 and 48 DF,  p-value: 0.01647

urca documentation built on May 2, 2019, 2:08 a.m.

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