summary-methods: Methods for Function summary in Package 'urca'

Description Methods Author(s) See Also Examples

Description

Summarises the outcome of unit root/cointegration tests by creating a new object of class sumurca.

Methods

object = "ur.df"

The test type, its statistic, the test regression and the critical values for the Augmented Dickey and Fuller test are returned.

object = "ur.ers"

The test type, its statistic and the critical values for the Elliott, Rothenberg \& Stock test are returned. In case of test "DF-GLS" the summary output of the test regression is provided, too.

object = "ur.kpss"

The test statistic, the critical value as well as the test type and the number of lags used for error correction for the Kwiatkowski et al. unit root test is returned.

object = "ca.jo"

The "trace" or "eigen" statistic, the critical values as well as the eigenvalues, eigenvectors and the loading matrix of the Johansen procedure are reported.

object = "cajo.test"

The test statistic of a restricted VAR with respect to \bold{α} and/or \bold{β} with p-value and degrees of freedom is reported. Furthermore, the restriction matrix(ces), the eigenvalues and eigenvectors as well as the loading matrix are returned.

object = "ca.po"

The "Pz" or "Pu" statistic, the critical values as well as the summary output of the test regression for the Phillips \& Ouliaris cointegration test.

object = "ur.pp"

The Z statistic, the critical values as well as the summary output of the test regression for the Phillips \& Perron test, as well as the test statistics for the coefficients of the deterministic part is returned.

object = "ur.df"

The relevant tau statistic, the critical values as well as the summary output of the test regression for the augmented Dickey-Fuller test is returned.

object = "ur.sp"

The test statistic, the critical value as well as the summary output of the test regression for the Schmidt \& Phillips test is returned.

object = "ur.za"

The test statistic, the critical values as well as the summary output of the test regression for the Zivot \& Andrews test is returned.

Author(s)

Bernhard Pfaff

See Also

ur.ers-class, ur.kpss-class, ca.jo-class, cajo.test-class, ca.po-class, ur.pp-class, ur.df-class, ur.sp-class, ur.za-class and sumurca-class.

Examples

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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)
#
kpss.gnp <- ur.kpss(gnp.l, type="tau", lags="short")
summary(kpss.gnp)
#
pp.gnp <- ur.pp(gnp, type="Z-tau", model="trend", lags="short")
summary(pp.gnp)
#
df.gnp <- ur.df(gnp, type="trend", lags=4)
summary(df.gnp)
#
sp.gnp <- ur.sp(gnp, type="tau", pol.deg=1, signif=0.01)
summary(sp.gnp)
#
za.gnp <- ur.za(gnp, model="both", lag=2)
summary(za.gnp)
#
data(finland)
sjf <- finland
sjf.vecm <- ca.jo(sjf, ecdet="none", type="eigen", K=2, season=4)
summary(sjf.vecm)
#
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))

Example output

############################################### 
# Elliot, Rothenberg and 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 
-44.314 -10.234   0.583  10.168  28.078 

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:
                 1pct  5pct 10pct
critical values -3.58 -3.03 -2.74


####################### 
# 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: 
                10pct  5pct 2.5pct  1pct
critical values 0.119 0.146  0.176 0.216


################################## 
# 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: 
                     1pct      5pct     10pct
critical values -4.113484 -3.483605 -3.169576


############################################### 
# 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 
-42.492  -9.887   0.912   9.861  25.634 

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: 
      1pct  5pct 10pct
tau3 -4.04 -3.45 -3.15
phi2  6.50  4.88  4.16
phi3  8.73  6.49  5.47


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


################################ 
# 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
  (3 observations deleted due to missingness)
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 


###################### 
# 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 and critical values of test:

          test 10pct  5pct  1pct
r <= 3 |  3.11  6.50  8.18 11.65
r <= 2 |  7.89 12.91 14.90 19.19
r <= 1 | 26.64 18.90 21.07 25.75
r = 0  | 38.49 24.78 27.14 32.14

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

           lrm1.l2    lny.l2    lnmr.l2    difp.l2
lrm1.l2  1.0000000  1.000000  1.0000000   1.000000
lny.l2  -0.9763252 -1.323191 -0.9199865   1.608739
lnmr.l2 -7.0910749 -2.016033  0.2691516  -1.375342
difp.l2 -7.0191097 22.740851 -1.8223931 -15.686927

Weights W:
(This is the loading matrix)

           lrm1.l2       lny.l2      lnmr.l2      difp.l2
lrm1.d 0.033342108 -0.020280528 -0.129947614 -0.002561906
lny.d  0.022544782 -0.005717446  0.012949130 -0.006265406
lnmr.d 0.053505000  0.046876449 -0.007367715  0.002173242
difp.d 0.005554849 -0.017353903  0.014561151  0.001531004


###################### 
# 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]
lrm1.d 0.0335 -0.0377 -0.1102
lny.d  0.0228 -0.0163  0.0238
lnmr.d 0.0543  0.0589 -0.0134
difp.d 0.0054 -0.0180  0.0113

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

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