R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("urca-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('urca')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "ablrtest"
> 
> ### * ablrtest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ablrtest
> ### Title: Likelihood ratio test for restrictions on alpha and beta
> ### Aliases: ablrtest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> HD1 <- matrix(c(1, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1), c(5,3))
> DA <- matrix(c(1,0,0,0, 0, 1, 0, 0, 0, 0, 0, 1), c(4,3))
> summary(ablrtest(sjd.vecm, H=HD1, A=DA, r=1))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under linear restrictions on alpha and beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1] [,2] [,3]
[1,]    1    0    0
[2,]   -1    0    0
[3,]    0    1    0
[4,]    0   -1    0
[5,]    0    0    1


     [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    0
[4,]    0    0    1

Eigenvalues of restricted VAR (lambda):
[1] 0.4100 0.0090 0.0053

The value of the likelihood ratio test statistic:
2.13 distributed as chi square with 2 df.
The p-value of the test statistic is: 0.35 

Eigenvectors, normalised to first column
of the restricted VAR:

        [,1]
[1,]  1.0000
[2,] -1.0000
[3,]  5.9508
[4,] -5.9508
[5,] -6.2162

Weights W of the restricted VAR:

        [,1]
[1,] -0.1519
[2,]  0.0992
[3,]  0.0000
[4,]  0.0288

> 
> 
> 
> cleanEx(); ..nameEx <- "alphaols"
> 
> ### * alphaols
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: alphaols
> ### Title: OLS regression of VECM weighting matrix
> ### Aliases: alphaols
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm1 <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> summary(alphaols(sjd.vecm1))
Response Y1 :

Call:
lm(formula = Y1 ~ -1 + RKV)

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

Coefficients:
       Estimate Std. Error   t value Pr(>|t|)    
RKV1 -2.130e-01  6.039e-02    -3.526 0.000938 ***
RKV2 -4.815e-03  4.028e-02    -0.120 0.905341    
RKV3  3.501e-02  2.184e-02     1.603 0.115453    
RKV4  2.029e-03  2.815e-03     0.721 0.474633    
RKV5 -1.251e-12  3.123e-02 -4.01e-11 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 Y2 :

Call:
lm(formula = Y2 ~ -1 + RKV)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.034479 -0.015065 -0.001000  0.011147  0.056657 

Coefficients:
      Estimate Std. Error  t value Pr(>|t|)  
RKV1 1.150e-01  6.189e-02    1.859   0.0692 .
RKV2 1.975e-02  4.128e-02    0.478   0.6345  
RKV3 4.994e-02  2.238e-02    2.231   0.0304 *
RKV4 1.109e-03  2.885e-03    0.384   0.7025  
RKV5 1.832e-13  3.200e-02 5.72e-12   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 Y3 :

Call:
lm(formula = Y3 ~ -1 + RKV)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.327e-02 -4.445e-03 -3.026e-05  4.853e-03  1.764e-02 

Coefficients:
       Estimate Std. Error  t value Pr(>|t|)
RKV1  2.318e-02  2.403e-02    0.965    0.340
RKV2 -1.060e-02  1.602e-02   -0.661    0.512
RKV3  3.480e-03  8.688e-03    0.401    0.691
RKV4 -1.574e-03  1.120e-03   -1.405    0.166
RKV5  5.399e-14  1.242e-02 4.35e-12    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 Y4 :

Call:
lm(formula = Y4 ~ -1 + RKV)

Residuals:
       Min         1Q     Median         3Q        Max 
-9.125e-03 -2.876e-03 -1.527e-05  2.458e-03  1.490e-02 

Coefficients:
       Estimate Std. Error  t value Pr(>|t|)   
RKV1  2.941e-02  1.524e-02    1.930  0.05949 . 
RKV2 -3.023e-02  1.016e-02   -2.975  0.00458 **
RKV3 -2.812e-03  5.510e-03   -0.510  0.61222   
RKV4 -4.768e-05  7.104e-04   -0.067  0.94677   
RKV5  9.114e-14  7.879e-03 1.16e-11  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 


> summary(alphaols(sjd.vecm1, reg.number=1))

Call:
lm(formula = R0[, reg.number] ~ -1 + RKV)

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

Coefficients:
       Estimate Std. Error   t value Pr(>|t|)    
RKV1 -2.130e-01  6.039e-02    -3.526 0.000938 ***
RKV2 -4.815e-03  4.028e-02    -0.120 0.905341    
RKV3  3.501e-02  2.184e-02     1.603 0.115453    
RKV4  2.029e-03  2.815e-03     0.721 0.474633    
RKV5 -1.251e-12  3.123e-02 -4.01e-11 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 

> 
> 
> 
> cleanEx(); ..nameEx <- "alrtest"
> 
> ### * alrtest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: alrtest
> ### Title: Likelihood ratio test for restrictions on alpha
> ### Aliases: alrtest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> DA <- matrix(c(1,0,0,0), c(4,1))
> summary(alrtest(sjd.vecm, A=DA, r=1))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under linear restrictions on beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1]
[1,]    1
[2,]    0
[3,]    0
[4,]    0

Eigenvalues of restricted VAR (lambda):
[1] 0.3573 0.0000 0.0000 0.0000 0.0000

The value of the likelihood ratio test statistic:
6.66 distributed as chi square with 3 df.
The p-value of the test statistic is: 0.08 

Eigenvectors, normalised to first column
of the restricted VAR:

       [,1]
LRM  1.0000
LRY -0.9585
IBO  4.7641
IDE -2.5708
    -6.5825

Weights W of the restricted VAR:

        [,1]
[1,] -0.2543
[2,]  0.0000
[3,]  0.0000
[4,]  0.0000

> 
> 
> 
> cleanEx(); ..nameEx <- "bh5lrtest"
> 
> ### * bh5lrtest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bh5lrtest
> ### Title: Likelihood ratio test for restrictions under partly known beta
> ### Aliases: bh5lrtest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(UKpppuip)
> attach(UKpppuip)
> dat1 <- cbind(p1, p2, e12, i1, i2)
> dat2 <- cbind(doilp0, doilp1)
> H1 <- ca.jo(dat1, type='trace', K=2, season=4, dumvar=dat2, ctable='A1')
> H51 <- c(1, -1, -1, 0, 0)
> H52 <- c(0, 0, 0, 1, -1)
> summary(bh5lrtest(H1, H=H51, r=2))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under partly known beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1]
[1,]    1
[2,]   -1
[3,]   -1
[4,]    0
[5,]    0

Eigenvalues of restricted VAR (lambda):
[1] 0.3956 0.2812 0.2541 0.1008

The value of the likelihood ratio test statistic:
14.52 distributed as chi square with 3 df.
The p-value of the test statistic is: 0 

Eigenvectors, normalised to first column
of the restricted VAR:

     [,1]     [,2]
[1,]    1   1.0000
[2,]   -1   0.7845
[3,]   -1   0.2155
[4,]    0 -64.9725
[5,]    0 -40.7031

Weights W of the restricted VAR:

        [,1]    [,2]
[1,] -0.0744 -0.0031
[2,] -0.0147 -0.0009
[3,]  0.0724  0.0057
[4,]  0.0164  0.0020
[5,]  0.0416  0.0035

> summary(bh5lrtest(H1, H=H52, r=2))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under partly known beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1]
[1,]    0
[2,]    0
[3,]    0
[4,]    1
[5,]   -1

Eigenvalues of restricted VAR (lambda):
[1] 0.4064 0.2607 0.1052 0.1007

The value of the likelihood ratio test statistic:
1.89 distributed as chi square with 3 df.
The p-value of the test statistic is: 0.59 

Eigenvectors, normalised to first column
of the restricted VAR:

     [,1]    [,2]
[1,]    0  1.0000
[2,]    0 -0.9102
[3,]    0 -0.9334
[4,]    1 -2.6163
[5,]   -1 -2.6163

Weights W of the restricted VAR:

        [,1]    [,2]
[1,]  0.0881 -0.0678
[2,] -0.0597 -0.0189
[3,] -0.2731  0.0975
[4,] -0.1450  0.0320
[5,]  0.2197  0.0625

> 
> 
> 
> cleanEx(); ..nameEx <- "bh6lrtest"
> 
> ### * bh6lrtest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bh6lrtest
> ### Title: Likelihood ratio test for restrictions under partly known beta
> ###   in a subspace
> ### Aliases: bh6lrtest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(UKpppuip)
> attach(UKpppuip)
> dat1 <- cbind(p1, p2, e12, i1, i2)
> dat2 <- cbind(doilp0, doilp1)
> H1 <- ca.jo(dat1, type='trace', K=2, season=4, dumvar=dat2, ctable='A1')
> H6 <- matrix(c(1,0,0,0,0, 0,1,0,0,0, 0,0,1,0,0,), c(5,3))
> bh6lrtest(z=H1, H=H6, r=2, r1=1, conv.val=0.0001, max.iter=50)

##################################################### 
# Johansen-Procedure Unit Root / Cointegration Test # 
##################################################### 

The value of the test statistic is: 4.9312 

> 
> 
> 
> cleanEx(); ..nameEx <- "blrtest"
> 
> ### * blrtest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: blrtest
> ### Title: Likelihood ratio test for restrictions on beta
> ### Aliases: blrtest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> HD0 <- matrix(c(-1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1), c(5,4))
> summary(blrtest(sjd.vecm, H=HD0, r=1))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under linear restrictions on beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1] [,2] [,3] [,4]
[1,]   -1    0    0    0
[2,]    1    0    0    0
[3,]    0    1    0    0
[4,]    0    0    1    0
[5,]    0    0    0    1

Eigenvalues of restricted VAR (lambda):
[1] 0.4327 0.1722 0.0436 0.0056

The value of the likelihood ratio test statistic:
0.04 distributed as chi square with 1 df.
The p-value of the test statistic is: 0.84 

Eigenvectors, normalised to first column
of the restricted VAR:

        [,1]    [,2]     [,3]    [,4]
[1,]  1.0000  1.0000   1.0000  1.0000
[2,] -1.0000 -1.0000  -1.0000 -1.0000
[3,]  5.3004  0.2293  99.7012  1.5513
[4,] -4.2904  8.9614 -51.8139 -2.0206
[5,] -6.2645 -6.6551 -13.4082 -5.8223

Weights W of the restricted VAR:

        [,1]    [,2]   [,3]    [,4]
[1,] -0.2120 -0.0195  4e-04  0.0131
[2,]  0.1075 -0.0061  2e-04  0.0196
[3,]  0.0226 -0.0097 -4e-04  0.0003
[4,]  0.0297 -0.0226  0e+00 -0.0021

> 
> 
> 
> cleanEx(); ..nameEx <- "ca.jo"
> 
> ### * ca.jo
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ca.jo
> ### Title: Johansen Procedure for VAR
> ### Aliases: ca.jo
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4, ctable="A3")
> summary(sjd.vecm)

###################### 
# Johansen-Procedure # 
###################### 

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

Eigenvalues (lambda):
[1]  4.331654e-01  1.775836e-01  1.127905e-01  4.341130e-02 -7.559584e-17

Values of teststatistic & critical values of test:

          test   10%    5%    1%
r <= 3 |  2.35  7.56  9.09 12.74
r <= 2 |  6.34 13.78 15.75 19.83
r <= 1 | 10.36 19.80 21.89 26.41
r = 0  | 30.09 25.61 28.17 33.12

Eigenvectors, normalised to first column:
(These are the cointegration relations)

              [,1]       [,2]       [,3]       [,4]       [,5]
LRM       1.000000  1.0000000  1.0000000   1.000000  1.0000000
LRY      -1.032949 -1.3681031 -3.2266580  -1.883625 -0.6336946
IBO       5.206919  0.2429825  0.5382847  24.399487  1.6965828
IDE      -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)

            [,1]        [,2]         [,3]          [,4]          [,5]
[1,] -0.21295494 -0.00481498  0.035011128  2.028908e-03 -2.265540e-13
[2,]  0.11502204  0.01975028  0.049938460  1.108654e-03  5.846654e-13
[3,]  0.02317724 -0.01059605  0.003480357 -1.573742e-03  3.523165e-14
[4,]  0.02941109 -0.03022917 -0.002811506 -4.767627e-05 -3.456735e-14

> #
> data(finland)
> sjf <- finland
> sjf.vecm <- ca.jo(sjf, constant=FALSE, type="eigen", K=2,
+ spec="longrun", season=4, ctable="A2")
> summary(sjf.vecm)

###################### 
# Johansen-Procedure # 
###################### 

Test type: maximal eigenvalue statistic (lambda max) , with linear trend 

Eigenvalues (lambda):
[1] 0.30932660 0.22599561 0.07308056 0.02946699

Values of teststatistic & critical values of test:

          test   10%    5%    1%
r <= 3 |  3.11  6.69  8.08 11.58
r <= 2 |  7.89 12.78 14.60 18.78
r <= 1 | 26.64 18.96 21.28 26.15
r = 0  | 38.49 24.92 27.34 32.62

Eigenvectors, normalised to first column:
(These are the cointegration relations)

           [,1]      [,2]       [,3]       [,4]
lrm1  1.0000000  1.000000  1.0000000   1.000000
lny  -0.9763252 -1.323191 -0.9199865   1.608739
lnmr -7.0910749 -2.016033  0.2691516  -1.375342
difp -7.0191097 22.740851 -1.8223931 -15.686927

Weights W:
(This is the loading matrix)

            [,1]         [,2]         [,3]         [,4]
[1,] 0.033342108 -0.020280528 -0.129947614 -0.002561906
[2,] 0.022544782 -0.005717446  0.012949130 -0.006265406
[3,] 0.053505000  0.046876449 -0.007367715  0.002173242
[4,] 0.005554849 -0.017353903  0.014561151  0.001531004

> 
> 
> 
> cleanEx(); ..nameEx <- "ca.po"
> 
> ### * ca.po
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ca.po
> ### Title: Phillips & Ouliaris Cointegration Test
> ### Aliases: ca.po
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(ecb)
> m3.real <- ecb[,"m3"]/ecb[,"gdp.defl"]
> gdp.real <- ecb[,"gdp.nom"]/ecb[,"gdp.defl"]
> rl <- ecb[,"rl"]
> ecb.data <- cbind(m3.real, gdp.real, rl)
> m3d.po <- ca.po(ecb.data, type="Pz")
> summary(m3d.po)

###################################### 
# Phillips & Ouliaris Unit Root Test # 
###################################### 

Test of type Pz 
detrending of series none 

Response m3.real :

Call:
lm(formula = m3.real ~ zr - 1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.578778 -0.261192 -0.007865  0.203497  1.065218 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
zrm3.real   0.99210    0.04147  23.920   <2e-16 ***
zrgdp.real  0.08627    0.16348   0.528    0.603    
zrrl       -0.09819    0.16534  -0.594    0.559    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.3617 on 22 degrees of freedom
Multiple R-Squared:     1,	Adjusted R-squared: 0.9999 
F-statistic: 1.584e+05 on 3 and 22 DF,  p-value: < 2.2e-16 


Response gdp.real :

Call:
lm(formula = gdp.real ~ zr - 1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.088196 -0.039820  0.005241  0.044033  0.091465 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
zrm3.real  -0.020408   0.005853  -3.487  0.00209 ** 
zrgdp.real  1.073163   0.023070  46.518  < 2e-16 ***
zrrl       -0.022009   0.023334  -0.943  0.35581    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.05104 on 22 degrees of freedom
Multiple R-Squared:     1,	Adjusted R-squared:     1 
F-statistic: 8.523e+05 on 3 and 22 DF,  p-value: < 2.2e-16 


Response rl :

Call:
lm(formula = rl ~ zr - 1)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.57215 -0.20139  0.04127  0.17227  0.59364 

Coefficients:
           Estimate Std. Error t value Pr(>|t|)    
zrm3.real  -0.05566    0.03661  -1.521 0.142616    
zrgdp.real  0.27091    0.14429   1.878 0.073765 .  
zrrl        0.64773    0.14594   4.438 0.000207 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.3192 on 22 degrees of freedom
Multiple R-Squared: 0.9962,	Adjusted R-squared: 0.9956 
F-statistic:  1906 on 3 and 22 DF,  p-value: < 2.2e-16 



Value of test-statistic is: 18.4658 

Critical values of Pz are:
                    10%      5%      1%
critical values 26.7022 32.9392 46.4097

> 
> 
> 
> cleanEx(); ..nameEx <- "cajolst"
> 
> ### * cajolst
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cajolst
> ### Title: Testing Cointegrating Rank with Level Shift at Unknown time
> ### Aliases: cajolst
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.lst <- cajolst(sjd, trend=TRUE, K=2, season=4)
> summary(sjd.lst)

###################### 
# Johansen-Procedure # 
###################### 

Test type: trace statistic , with linear trend in shift correction 

Eigenvalues (lambda):
[1] 0.42098147 0.27098513 0.17330604 0.06127991

Values of teststatistic & critical values of test:

          test   10%    5%    1%
r <= 3 |  3.15  5.42  6.79 10.04
r <= 2 | 11.62 13.78 15.83 19.85
r <= 1 | 24.33 25.93 28.45 33.76
r = 0  | 42.95 42.08 45.20 51.60

Eigenvectors, normalised to first column:
(These are the cointegration relations)

         [,1]       [,2]       [,3]       [,4]
LRM 1.0000000   1.000000  1.0000000  1.0000000
LRY 0.8490645  -2.319498 -1.8603632 -0.2148260
IBO 6.0747337   6.824430  0.8571653  0.4685797
IDE 1.0858006 -11.662840  2.7346259 -0.5253649

Weights W:
(This is the loading matrix)

             [,1]         [,2]        [,3]         [,4]
[1,] -0.146180842 -0.034940907  0.04306167 -0.066397980
[2,] -0.081222325  0.090040394  0.10130486 -0.011416802
[3,] -0.021090906  0.002883555 -0.01985965  0.030806000
[4,]  0.004947721  0.022143257 -0.03940262  0.008027878

> 
> 
> 
> cleanEx(); ..nameEx <- "cajools"
> 
> ### * cajools
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cajools
> ### Title: OLS regression of VECM
> ### Aliases: cajools
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm1 <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> sjd.vecm2 <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="transitory",
+ season=4)
> sjd.vecm.ols1 <- cajools(sjd.vecm1)
> sjd.vecm.ols2 <- cajools(sjd.vecm2)
> summary(sjd.vecm.ols1)
Response Y1 :

Call:
lm(formula = Y1 ~ z@Z1 + z@ZK - 1)

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

Coefficients:
         Estimate Std. Error t value Pr(>|t|)    
z@Z11    0.014228   0.201655   0.071  0.94409    
z@Z12    0.013753   0.166549   0.083  0.93459    
z@Z13   -1.180148   0.393173  -3.002  0.00456 ** 
z@Z14    0.176409   0.598347   0.295  0.76961    
z@Z15   -0.055917   0.010563  -5.294 4.34e-06 ***
z@Z16   -0.016458   0.009426  -1.746  0.08831 .  
z@Z17   -0.039480   0.008961  -4.406 7.40e-05 ***
z@ZKLRM -0.180730   0.088757  -2.036  0.04822 *  
z@ZKLRY  0.109768   0.120060   0.914  0.36592    
z@ZKIBO -1.041659   0.353320  -2.948  0.00526 ** 
z@ZKIDE  0.638122   0.434247   1.469  0.14933    
z@ZK     1.582925   0.547678   2.890  0.00613 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02165 on 41 degrees of freedom
Multiple R-Squared: 0.6804,	Adjusted R-squared: 0.5868 
F-statistic: 7.273 on 12 and 41 DF,  p-value: 6.759e-07 


Response Y2 :

Call:
lm(formula = Y2 ~ z@Z1 + z@ZK - 1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.034479 -0.015065 -0.001000  0.011147  0.056657 

Coefficients:
         Estimate Std. Error t value Pr(>|t|)   
z@Z11    0.689838   0.206656   3.338  0.00180 **
z@Z12   -0.353616   0.170679  -2.072  0.04461 * 
z@Z13    0.280519   0.402923   0.696  0.49023   
z@Z14   -0.587402   0.613185  -0.958  0.34370   
z@Z15   -0.025121   0.010825  -2.321  0.02536 * 
z@Z16    0.007339   0.009660   0.760  0.45179   
z@Z17   -0.011369   0.009183  -1.238  0.22276   
z@ZKLRM  0.185819   0.090958   2.043  0.04752 * 
z@ZKLRY -0.309055   0.123038  -2.512  0.01604 * 
z@ZKIBO  0.657641   0.362082   1.816  0.07664 . 
z@ZKIDE -0.647679   0.445015  -1.455  0.15317   
z@ZK    -0.389553   0.561260  -0.694  0.49155   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02218 on 41 degrees of freedom
Multiple R-Squared: 0.4015,	Adjusted R-squared: 0.2264 
F-statistic: 2.292 on 12 and 41 DF,  p-value: 0.02421 


Response Y3 :

Call:
lm(formula = Y3 ~ z@Z1 + z@ZK - 1)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.327e-02 -4.445e-03 -3.026e-05  4.853e-03  1.764e-02 

Coefficients:
          Estimate Std. Error t value Pr(>|t|)  
z@Z11    0.0654218  0.0802292   0.815   0.4195  
z@Z12    0.1179269  0.0662622   1.780   0.0825 .
z@Z13    0.3825684  0.1564254   2.446   0.0188 *
z@Z14    0.0858928  0.2380548   0.361   0.7201  
z@Z15   -0.0000689  0.0042027  -0.016   0.9870  
z@Z16    0.0073995  0.0037503   1.973   0.0553 .
z@Z17    0.0048269  0.0035652   1.354   0.1832  
z@ZKLRM  0.0144878  0.0353122   0.410   0.6837  
z@ZKLRY -0.0177100  0.0477665  -0.371   0.7127  
z@ZKIBO  0.0815823  0.1405700   0.580   0.5648  
z@ZKIDE -0.1673547  0.1727669  -0.969   0.3384  
z@ZK    -0.0641545  0.2178960  -0.294   0.7699  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.008613 on 41 degrees of freedom
Multiple R-Squared: 0.3992,	Adjusted R-squared: 0.2234 
F-statistic:  2.27 on 12 and 41 DF,  p-value: 0.02555 


Response Y4 :

Call:
lm(formula = Y4 ~ z@Z1 + z@ZK - 1)

Residuals:
       Min         1Q     Median         3Q        Max 
-9.125e-03 -2.876e-03 -1.527e-05  2.458e-03  1.490e-02 

Coefficients:
         Estimate Std. Error t value Pr(>|t|)    
z@Z11    0.065001   0.050881   1.278 0.208607    
z@Z12   -0.001606   0.042023  -0.038 0.969697    
z@Z13    0.370309   0.099203   3.733 0.000576 ***
z@Z14   -0.049376   0.150972  -0.327 0.745292    
z@Z15   -0.004189   0.002665  -1.572 0.123709    
z@Z16   -0.001087   0.002378  -0.457 0.650085    
z@Z17   -0.002730   0.002261  -1.208 0.234120    
z@ZKLRM -0.003677   0.022395  -0.164 0.870378    
z@ZKLRY  0.020138   0.030293   0.665 0.509916    
z@ZKIBO  0.143119   0.089148   1.605 0.116079    
z@ZKIDE -0.314235   0.109567  -2.868 0.006498 ** 
z@ZK    -0.071218   0.138187  -0.515 0.609062    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.005462 on 41 degrees of freedom
Multiple R-Squared: 0.507,	Adjusted R-squared: 0.3627 
F-statistic: 3.514 on 12 and 41 DF,  p-value: 0.001273 


> summary(sjd.vecm.ols2)
Response Y1 :

Call:
lm(formula = Y1 ~ z@Z1 + z@ZK - 1)

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

Coefficients:
         Estimate Std. Error t value Pr(>|t|)    
z@Z11    0.194958   0.176615   1.104  0.27609    
z@Z12   -0.096016   0.157827  -0.608  0.54630    
z@Z13   -0.138489   0.436917  -0.317  0.75288    
z@Z14   -0.461713   0.576711  -0.801  0.42798    
z@Z15   -0.055917   0.010563  -5.294 4.34e-06 ***
z@Z16   -0.016458   0.009426  -1.746  0.08831 .  
z@Z17   -0.039480   0.008961  -4.406 7.40e-05 ***
z@ZKLRM -0.180730   0.088757  -2.036  0.04822 *  
z@ZKLRY  0.109768   0.120060   0.914  0.36592    
z@ZKIBO -1.041659   0.353320  -2.948  0.00526 ** 
z@ZKIDE  0.638122   0.434247   1.469  0.14933    
z@ZK     1.582925   0.547678   2.890  0.00613 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02165 on 41 degrees of freedom
Multiple R-Squared: 0.6804,	Adjusted R-squared: 0.5868 
F-statistic: 7.273 on 12 and 41 DF,  p-value: 6.759e-07 


Response Y2 :

Call:
lm(formula = Y2 ~ z@Z1 + z@ZK - 1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.034479 -0.015065 -0.001000  0.011147  0.056657 

Coefficients:
         Estimate Std. Error t value Pr(>|t|)   
z@Z11    0.504019   0.180994   2.785  0.00807 **
z@Z12   -0.044561   0.161741  -0.276  0.78431   
z@Z13   -0.377122   0.447752  -0.842  0.40453   
z@Z14    0.060277   0.591012   0.102  0.91926   
z@Z15   -0.025121   0.010825  -2.321  0.02536 * 
z@Z16    0.007339   0.009660   0.760  0.45179   
z@Z17   -0.011369   0.009183  -1.238  0.22276   
z@ZKLRM  0.185819   0.090958   2.043  0.04752 * 
z@ZKLRY -0.309055   0.123038  -2.512  0.01604 * 
z@ZKIBO  0.657641   0.362082   1.816  0.07664 . 
z@ZKIDE -0.647679   0.445015  -1.455  0.15317   
z@ZK    -0.389553   0.561260  -0.694  0.49155   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.02218 on 41 degrees of freedom
Multiple R-Squared: 0.4015,	Adjusted R-squared: 0.2264 
F-statistic: 2.292 on 12 and 41 DF,  p-value: 0.02421 


Response Y3 :

Call:
lm(formula = Y3 ~ z@Z1 + z@ZK - 1)

Residuals:
       Min         1Q     Median         3Q        Max 
-2.327e-02 -4.445e-03 -3.026e-05  4.853e-03  1.764e-02 

Coefficients:
          Estimate Std. Error t value Pr(>|t|)  
z@Z11    0.0509340  0.0702669   0.725   0.4727  
z@Z12    0.1356369  0.0627923   2.160   0.0367 *
z@Z13    0.3009861  0.1738292   1.732   0.0909 .
z@Z14    0.2532475  0.2294467   1.104   0.2761  
z@Z15   -0.0000689  0.0042027  -0.016   0.9870  
z@Z16    0.0073995  0.0037503   1.973   0.0553 .
z@Z17    0.0048269  0.0035652   1.354   0.1832  
z@ZKLRM  0.0144878  0.0353122   0.410   0.6837  
z@ZKLRY -0.0177100  0.0477665  -0.371   0.7127  
z@ZKIBO  0.0815823  0.1405700   0.580   0.5648  
z@ZKIDE -0.1673547  0.1727669  -0.969   0.3384  
z@ZK    -0.0641545  0.2178960  -0.294   0.7699  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.008613 on 41 degrees of freedom
Multiple R-Squared: 0.3992,	Adjusted R-squared: 0.2234 
F-statistic:  2.27 on 12 and 41 DF,  p-value: 0.02555 


Response Y4 :

Call:
lm(formula = Y4 ~ z@Z1 + z@ZK - 1)

Residuals:
       Min         1Q     Median         3Q        Max 
-9.125e-03 -2.876e-03 -1.527e-05  2.458e-03  1.490e-02 

Coefficients:
         Estimate Std. Error t value Pr(>|t|)   
z@Z11    0.068678   0.044563   1.541   0.1310   
z@Z12   -0.021744   0.039822  -0.546   0.5880   
z@Z13    0.227189   0.110241   2.061   0.0457 * 
z@Z14    0.264860   0.145513   1.820   0.0760 . 
z@Z15   -0.004189   0.002665  -1.572   0.1237   
z@Z16   -0.001087   0.002378  -0.457   0.6501   
z@Z17   -0.002730   0.002261  -1.208   0.2341   
z@ZKLRM -0.003677   0.022395  -0.164   0.8704   
z@ZKLRY  0.020138   0.030293   0.665   0.5099   
z@ZKIBO  0.143119   0.089148   1.605   0.1161   
z@ZKIDE -0.314235   0.109567  -2.868   0.0065 **
z@ZK    -0.071218   0.138187  -0.515   0.6091   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.005462 on 41 degrees of freedom
Multiple R-Squared: 0.507,	Adjusted R-squared: 0.3627 
F-statistic: 3.514 on 12 and 41 DF,  p-value: 0.001273 


> 
> 
> 
> cleanEx(); ..nameEx <- "lttest"
> 
> ### * lttest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lttest
> ### Title: Likelihood ratio test for no linear trend in VAR
> ### Aliases: lttest
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- as.matrix(denmark[, c("LRM", "LRY", "IBO", "IDE")])
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> lttest(sjd.vecm, r=1)
LR-test for no linear trend

H0: H*2(r<=1)
H1: H2(r<=1)

Test statistic is distributed as chi-square
with 3 degress of freedom
        test statistic p-value
LR test           1.98    0.58
> #
> data(finland)
> sjf <- as.matrix(finland)
> sjf.vecm <- ca.jo(sjf, constant=FALSE, type="eigen", K=2,
+ spec="longrun", season=4)
> lttest(sjf.vecm, r=3)
LR-test for no linear trend

H0: H*2(r<=3)
H1: H2(r<=3)

Test statistic is distributed as chi-square
with 1 degress of freedom
        test statistic p-value
LR test           4.78    0.03
> 
> 
> 
> cleanEx(); ..nameEx <- "plot-methods"
> 
> ### * plot-methods
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot-methods
> ### Title: Methods for Function plot in Package `urca'
> ### Aliases: plot plot-methods plot,ur.ers,missing-method
> ###   plot,ur.kpss,missing-method plot,ca.jo,missing-method
> ###   plot,ca.po,missing-method plot,ur.pp,missing-method
> ###   plot,ur.sp,missing-method plot,ur.za,missing-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> gnp.l <- log(gnp)
> #
> ers.gnp <- ur.ers(gnp, type="DF-GLS", model="trend", lag.max=4)
> plot(ers.gnp)
> #
> kpss.gnp <- ur.kpss(gnp.l, type="tau", lags="short")
> plot(kpss.gnp)
> #
> pp.gnp <- ur.pp(gnp, type="Z-tau", model="trend", lags="short")
> plot(pp.gnp)
> #
> sp.gnp <- ur.sp(gnp, type="tau", pol.deg=1, signif=0.01)
> plot(sp.gnp)
> #
> za.gnp <- ur.za(gnp, model="both", lag=2)
> plot(za.gnp)
> #
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, season=4)
> plot(sjd.vecm)
> 
> 
> 
> cleanEx(); ..nameEx <- "plotres"
> 
> ### * plotres
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plotres
> ### Title: Graphical inspection of VECM residuals
> ### Aliases: plotres
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, spec="longrun",
+ season=4)
> plotres(sjd.vecm)
> 
> 
> 
> cleanEx(); ..nameEx <- "show-methods"
> 
> ### * show-methods
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: show-methods
> ### Title: Methods for Function show in Package `urca'
> ### Aliases: show show-methods show,ur.ers-method show,ur.kpss-method
> ###   show,ca.jo-method show,ca.po-method show,cajo.test-method
> ###   show,ur.pp-method show,ur.df-method show,ur.sp-method
> ###   show,ur.za-method show,sumurca-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> gnp.l <- log(gnp)
> #
> ers.gnp <- ur.ers(gnp, type="DF-GLS", model="trend", lag.max=4)
> show(ers.gnp)

############################################################# 
# Elliot, Rothenberg & Stock Unit Root / Cointegration Test # 
############################################################# 

The value of the test statistic is: -0.9499 

> #
> kpss.gnp <- ur.kpss(gnp.l, type="tau", lags="short")
> show(kpss.gnp)

####################################### 
# KPSS Unit Root / Cointegration Test # 
####################################### 

The value of the test statistic is: 0.1976 

> #
> pp.gnp <- ur.pp(gnp, type="Z-tau", model="trend", lags="short")
> show(pp.gnp)

################################################## 
# Phillips-Perron Unit Root / Cointegration Test # 
################################################## 

The value of the test statistic is: -0.7734 

> #
> df.gnp <- ur.df(gnp, type="trend", lags=4)
> show(df.gnp)

############################################################### 
# Augmented Dickey-Fuller Test Unit Root / Cointegration Test # 
############################################################### 

The value of the test statistic is: -0.6614 4.2327 3.2833 

> #
> sp.gnp <- ur.sp(gnp, type="tau", pol.deg=1, signif=0.01)
> show(sp.gnp)

################################################### 
# Schmidt-Phillips Unit Root / Cointegration Test # 
################################################### 

The value of the test statistic is: -1.3732 

> #
> za.gnp <- ur.za(gnp, model="both", lag=2)
> show(za.gnp)

################################################ 
# Zivot-Andrews Unit Root / Cointegration Test # 
################################################ 

The value of the test statistic is: -3.8431 

> #
> data(denmark)
> sjd <- denmark[, c("LRM", "LRY", "IBO", "IDE")]
> sjd.vecm <- ca.jo(sjd, constant=TRUE, type="eigen", K=2, season=4)
> show(sjd.vecm)

##################################################### 
# Johansen-Procedure Unit Root / Cointegration Test # 
##################################################### 

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

> #
> HD0 <- matrix(c(-1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1), c(5,4))
> show(blrtest(sjd.vecm, H=HD0, r=1))

##################################################### 
# Johansen-Procedure Unit Root / Cointegration Test # 
##################################################### 

The value of the test statistic is: 0.0432 

> 
> 
> 
> cleanEx(); ..nameEx <- "summary-methods"
> 
> ### * summary-methods
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary-methods
> ### Title: Methods for Function summary in Package `urca'
> ### Aliases: summary summary-methods summary,ur.ers-method
> ###   summary,ur.kpss-method summary,ca.jo-method summary,cajo.test-method
> ###   summary,ca.po-method summary,ur.pp-method summary,ur.df-method
> ###   summary,ur.sp-method summary,ur.za-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> gnp.l <- log(gnp)
> #
> ers.gnp <- ur.ers(gnp, type="DF-GLS", model="trend", lag.max=4)
> summary(ers.gnp)

############################################# 
# Elliot, Rothenberg & Stock Unit Root Test # 
############################################# 

Test of type DF-GLS 
detrending of series with intercept and trend 


Call:
lm(formula = dfgls.form, data = data.dfgls)

Residuals:
     Min       1Q   Median       3Q      Max 
-44.3137 -10.2342   0.5835  10.1685  28.0779 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
yd.lag       -0.034122   0.035922  -0.950  0.34656   
yd.diff.lag1  0.452478   0.139331   3.247  0.00204 **
yd.diff.lag2  0.085861   0.152483   0.563  0.57580   
yd.diff.lag3 -0.008207   0.153899  -0.053  0.95767   
yd.diff.lag4 -0.082233   0.144692  -0.568  0.57226   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.86 on 52 degrees of freedom
Multiple R-Squared: 0.2294,	Adjusted R-squared: 0.1553 
F-statistic: 3.095 on 5 and 52 DF,  p-value: 0.01609 


Value of test-statistic is: -0.9499 

Critical values of DF-GLS are:
                   1%    5%   10%
critical values -3.58 -3.03 -2.74

> #
> kpss.gnp <- ur.kpss(gnp.l, type="tau", lags="short")
> summary(kpss.gnp)

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: tau with 3 lags. 

Value of test-statistic is: 0.1976 

Critical value for a significance level of: 
                  10%    5%  2.5%    1%
critical values 0.119 0.146 0.176 0.216

> #
> pp.gnp <- ur.pp(gnp, type="Z-tau", model="trend", lags="short")
> summary(pp.gnp)

################################## 
# Phillips-Perron Unit Root Test # 
################################## 

Test regression with intercept and trend 


Call:
lm(formula = y ~ y.l1 + trend)

Residuals:
    Min      1Q  Median      3Q     Max 
-54.683  -8.176   2.394  11.843  27.884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 14.01374    9.93593   1.410    0.164    
y.l1         0.98538    0.03301  29.849   <2e-16 ***
trend        0.50203    0.32292   1.555    0.125    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.75 on 58 degrees of freedom
Multiple R-Squared: 0.9926,	Adjusted R-squared: 0.9924 
F-statistic:  3896 on 2 and 58 DF,  p-value: < 2.2e-16 


Value of test-statistic, type: Z-tau  is: -0.7734 

           aux. Z statistics
Z-tau-mu              0.7316
Z-tau-beta            1.6657

Critical values for Z statistics: 
                       1%        5%       10%
critical values -4.113484 -3.483605 -3.169576

> #
> df.gnp <- ur.df(gnp, type="trend", lags=4)
> summary(df.gnp)

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
     Min       1Q   Median       3Q      Max 
-42.4921  -9.8872   0.9124   9.8612  25.6340 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) -2.71394    4.63380  -0.586    0.561  
z.lag.1     -0.02785    0.04211  -0.661    0.511  
tt           0.61613    0.38509   1.600    0.116  
z.diff.lag1  0.33761    0.14502   2.328    0.024 *
z.diff.lag2  0.02606    0.15108   0.173    0.864  
z.diff.lag3 -0.05841    0.15099  -0.387    0.701  
z.diff.lag4 -0.19280    0.15010  -1.284    0.205  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.31 on 50 degrees of freedom
Multiple R-Squared: 0.3033,	Adjusted R-squared: 0.2197 
F-statistic: 3.628 on 6 and 50 DF,  p-value: 0.004582 


Value of test-statistic is: -0.6614 4.2327 3.2833 

Critical values for test statistics: 
        1%    5%   10%
tau3 -4.04 -3.45 -3.15
phi2  6.50  4.88  4.16
phi3  8.73  6.49  5.47

> #
> sp.gnp <- ur.sp(gnp, type="tau", pol.deg=1, signif=0.01)
> summary(sp.gnp)

################################### 
# Schmidt-Phillips Unit Root Test # 
################################### 


Call:
lm(formula = sp.data)

Residuals:
    Min      1Q  Median      3Q     Max 
-54.683  -8.176   2.394  11.843  27.884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.80008    4.18871  -0.430    0.669    
y.lagged     0.98538    0.03301  29.849   <2e-16 ***
trend.exp1   0.50203    0.32292   1.555    0.125    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.75 on 58 degrees of freedom
Multiple R-Squared: 0.9926,	Adjusted R-squared: 0.9924 
F-statistic:  3896 on 2 and 58 DF,  p-value: < 2.2e-16 


Value of test-statistic is: -1.3732 
Critical value for a significance level of 0.01 
is: -3.63 

> #
> za.gnp <- ur.za(gnp, model="both", lag=2)
> summary(za.gnp)

################################ 
# Zivot-Andrews Unit Root Test # 
################################ 


Call:
lm(formula = testmat)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.753  -9.413   2.138   9.934  22.977 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.49068   10.25301   2.096  0.04096 *  
y.l1          0.77341    0.05896  13.118  < 2e-16 ***
trend         1.19804    0.66346   1.806  0.07675 .  
y.dl1         0.39699    0.12608   3.149  0.00272 ** 
y.dl2         0.10503    0.13401   0.784  0.43676    
du          -25.44710    9.20734  -2.764  0.00788 ** 
dt            2.11456    0.84179   2.512  0.01515 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 13.72 on 52 degrees of freedom
Multiple R-Squared: 0.9948,	Adjusted R-squared: 0.9942 
F-statistic:  1651 on 6 and 52 DF,  p-value: < 2.2e-16 


Teststatistic: -3.8431 
Critical values: 0.01= -5.57 0.05= -5.08 0.1= -4.82 

Potential break point at position: 21 

> #
> data(finland)
> sjf <- finland
> sjf.vecm <- ca.jo(sjf, constant=FALSE, type="eigen", K=2, season=4)
> summary(sjf.vecm)

###################### 
# Johansen-Procedure # 
###################### 

Test type: maximal eigenvalue statistic (lambda max) , with linear trend 

Eigenvalues (lambda):
[1] 0.30932660 0.22599561 0.07308056 0.02946699

Values of teststatistic & critical values of test:

          test   10%    5%    1%
r <= 3 |  3.11  2.82  3.96  6.94
r <= 2 |  7.89 12.10 14.04 17.94
r <= 1 | 26.64 18.70 20.78 25.52
r = 0  | 38.49 24.71 27.17 31.94

Eigenvectors, normalised to first column:
(These are the cointegration relations)

           [,1]      [,2]       [,3]       [,4]
lrm1  1.0000000  1.000000  1.0000000   1.000000
lny  -0.9763252 -1.323191 -0.9199865   1.608739
lnmr -7.0910749 -2.016033  0.2691516  -1.375342
difp -7.0191097 22.740851 -1.8223931 -15.686927

Weights W:
(This is the loading matrix)

            [,1]         [,2]         [,3]         [,4]
[1,] 0.033342108 -0.020280528 -0.129947614 -0.002561906
[2,] 0.022544782 -0.005717446  0.012949130 -0.006265406
[3,] 0.053505000  0.046876449 -0.007367715  0.002173242
[4,] 0.005554849 -0.017353903  0.014561151  0.001531004

> #
> HF0 <- matrix(c(-1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1), c(4,3))
> summary(blrtest(sjf.vecm, H=HF0, r=3))

###################### 
# Johansen-Procedure # 
###################### 

Estimation and testing under linear restrictions on beta 

The VECM has been estimated subject to: 
beta=H*phi and/or alpha=A*psi

     [,1] [,2] [,3]
[1,]   -1    0    0
[2,]    1    0    0
[3,]    0    1    0
[4,]    0    0    1

Eigenvalues of restricted VAR (lambda):
[1] 0.3093 0.1994 0.0705

The value of the likelihood ratio test statistic:
3.82 distributed as chi square with 3 df.
The p-value of the test statistic is: 0.28 

Eigenvectors, normalised to first column
of the restricted VAR:

       [,1]    [,2]    [,3]
[1,]  1.000  1.0000  1.0000
[2,] -1.000 -1.0000 -1.0000
[3,] -7.090 -1.4409  0.3503
[4,] -6.288 14.4392 -1.6555

Weights W of the restricted VAR:

       [,1]    [,2]    [,3]
[1,] 0.0335 -0.0377 -0.1102
[2,] 0.0228 -0.0163  0.0238
[3,] 0.0543  0.0589 -0.0134
[4,] 0.0054 -0.0180  0.0113

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.df"
> 
> ### * ur.df
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.df
> ### Title: Augmented-Dickey-Fuller Unit Root Test
> ### Aliases: ur.df
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(Raotbl3)
> attach(Raotbl3)
> lc.df <- ur.df(y=lc, lags=3, type='trend')
> summary(lc.df)

############################################### 
# Augmented Dickey-Fuller Test Unit Root Test # 
############################################### 

Test regression trend 


Call:
lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0447139 -0.0065246  0.0001288  0.0062253  0.0453532 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept)  0.7976591  0.3547775   2.248   0.0270 * 
z.lag.1     -0.0758706  0.0338880  -2.239   0.0277 * 
tt           0.0004915  0.0002159   2.277   0.0252 * 
z.diff.lag1 -0.1063957  0.1006744  -1.057   0.2934   
z.diff.lag2  0.2011373  0.1012373   1.987   0.0500 . 
z.diff.lag3  0.2998586  0.1020548   2.938   0.0042 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.01307 on 89 degrees of freedom
Multiple R-Squared: 0.1472,	Adjusted R-squared: 0.09924 
F-statistic: 3.071 on 5 and 89 DF,  p-value: 0.01325 


Value of test-statistic is: -2.2389 3.7382 2.5972 

Critical values for test statistics: 
        1%    5%   10%
tau3 -4.04 -3.45 -3.15
phi2  6.50  4.88  4.16
phi3  8.73  6.49  5.47

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.ers"
> 
> ### * ur.ers
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.ers
> ### Title: Elliott, Rothenberg & Stock Unit Root Test
> ### Aliases: ur.ers
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> ers.gnp <- ur.ers(gnp, type="DF-GLS", model="const", lag.max=4)
> summary(ers.gnp)

############################################# 
# Elliot, Rothenberg & Stock Unit Root Test # 
############################################# 

Test of type DF-GLS 
detrending of series with intercept 


Call:
lm(formula = dfgls.form, data = data.dfgls)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.767  -6.011   4.775  14.896  31.454 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)   
yd.lag        0.02559    0.01793   1.427  0.15962   
yd.diff.lag1  0.45630    0.14668   3.111  0.00303 **
yd.diff.lag2  0.06223    0.15879   0.392  0.69672   
yd.diff.lag3 -0.02445    0.15965  -0.153  0.87886   
yd.diff.lag4 -0.10768    0.15110  -0.713  0.47925   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 16.49 on 52 degrees of freedom
Multiple R-Squared: 0.3825,	Adjusted R-squared: 0.3231 
F-statistic: 6.442 on 5 and 52 DF,  p-value: 9.956e-05 


Value of test-statistic is: 1.4268 

Critical values of DF-GLS are:
                  1%    5%   10%
critical values -2.6 -1.95 -1.62

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.kpss"
> 
> ### * ur.kpss
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.kpss
> ### Title: Kwiatkowski et al. Unit Root Test
> ### Aliases: ur.kpss
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> gnp.l <- log(gnp)
> kpss.gnp <- ur.kpss(gnp.l, type="tau", lags="short")
> summary(kpss.gnp)

####################### 
# KPSS Unit Root Test # 
####################### 

Test is of type: tau with 3 lags. 

Value of test-statistic is: 0.1976 

Critical value for a significance level of: 
                  10%    5%  2.5%    1%
critical values 0.119 0.146 0.176 0.216

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.pp"
> 
> ### * ur.pp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.pp
> ### Title: Phillips & Perron Unit Root Test
> ### Aliases: ur.pp
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> pp.gnp <- ur.pp(gnp, type="Z-tau", model="trend", lags="short")
> summary(pp.gnp)

################################## 
# Phillips-Perron Unit Root Test # 
################################## 

Test regression with intercept and trend 


Call:
lm(formula = y ~ y.l1 + trend)

Residuals:
    Min      1Q  Median      3Q     Max 
-54.683  -8.176   2.394  11.843  27.884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 14.01374    9.93593   1.410    0.164    
y.l1         0.98538    0.03301  29.849   <2e-16 ***
trend        0.50203    0.32292   1.555    0.125    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.75 on 58 degrees of freedom
Multiple R-Squared: 0.9926,	Adjusted R-squared: 0.9924 
F-statistic:  3896 on 2 and 58 DF,  p-value: < 2.2e-16 


Value of test-statistic, type: Z-tau  is: -0.7734 

           aux. Z statistics
Z-tau-mu              0.7316
Z-tau-beta            1.6657

Critical values for Z statistics: 
                       1%        5%       10%
critical values -4.113484 -3.483605 -3.169576

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.sp"
> 
> ### * ur.sp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.sp
> ### Title: Schmidt & Phillips Unit Root Test
> ### Aliases: ur.sp
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> sp.gnp <- ur.sp(gnp, type="tau", pol.deg=1, signif=0.01)
> summary(sp.gnp)

################################### 
# Schmidt-Phillips Unit Root Test # 
################################### 


Call:
lm(formula = sp.data)

Residuals:
    Min      1Q  Median      3Q     Max 
-54.683  -8.176   2.394  11.843  27.884 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.80008    4.18871  -0.430    0.669    
y.lagged     0.98538    0.03301  29.849   <2e-16 ***
trend.exp1   0.50203    0.32292   1.555    0.125    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 15.75 on 58 degrees of freedom
Multiple R-Squared: 0.9926,	Adjusted R-squared: 0.9924 
F-statistic:  3896 on 2 and 58 DF,  p-value: < 2.2e-16 


Value of test-statistic is: -1.3732 
Critical value for a significance level of 0.01 
is: -3.63 

> 
> 
> 
> cleanEx(); ..nameEx <- "ur.za"
> 
> ### * ur.za
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ur.za
> ### Title: Zivot & Andrews Unit Root Test
> ### Aliases: ur.za
> ### Keywords: regression
> 
> ### ** Examples
> 
> data(nporg)
> gnp <- na.omit(nporg[, "gnp.r"])
> za.gnp <- ur.za(gnp, model="both", lag=2)
> summary(za.gnp)

################################ 
# Zivot-Andrews Unit Root Test # 
################################ 


Call:
lm(formula = testmat)

Residuals:
    Min      1Q  Median      3Q     Max 
-39.753  -9.413   2.138   9.934  22.977 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  21.49068   10.25301   2.096  0.04096 *  
y.l1          0.77341    0.05896  13.118  < 2e-16 ***
trend         1.19804    0.66346   1.806  0.07675 .  
y.dl1         0.39699    0.12608   3.149  0.00272 ** 
y.dl2         0.10503    0.13401   0.784  0.43676    
du          -25.44710    9.20734  -2.764  0.00788 ** 
dt            2.11456    0.84179   2.512  0.01515 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 13.72 on 52 degrees of freedom
Multiple R-Squared: 0.9948,	Adjusted R-squared: 0.9942 
F-statistic:  1651 on 6 and 52 DF,  p-value: < 2.2e-16 


Teststatistic: -3.8431 
Critical values: 0.01= -5.57 0.05= -5.08 0.1= -4.82 

Potential break point at position: 21 

> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  9.85 0.2 10.25 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')