Methods for Function summary in Package `urca'
summary-methods.RdSummarises 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 and 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 \(\bold{\alpha}\) and/or \(\bold{\beta}\) 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 and 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 and 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 and 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 and Andrews test is returned.
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 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.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:
#> 10pct 5pct 2.5pct 1pct
#> 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:
#> 1pct 5pct 10pct
#> 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
#> -42.492 -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
#>
#
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
#> (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
#>
#
data(finland)
sjf <- finland
sjf.vecm <- ca.jo(sjf, ecdet="none", 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 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
#>
#
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]
#> 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
#>