ca.po: Phillips & Ouliaris Cointegration Test

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

View source: R/ca-po.R

Description

Performs the Phillips \& Ouliaris "Pu" and "Pz" cointegration test.

Usage

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ca.po(z, demean = c("none", "constant", "trend"),
      lag = c("short", "long"), type = c("Pu", "Pz"), tol = NULL)

Arguments

z

Data matrix to be investigated for cointegration.

demean

The method for detrending the series, either "none", "constant" or "trend".

lag

Either a short or long lag number used for variance/covariance correction.

type

The test type, either "Pu" or "Pz".

tol

Numeric, this argument is passed to solve() in ca.po().

Details

The test "Pz", compared to the test "Pu", has the advantage that it is invariant to the normalization of the cointegration vector, i.e. it does not matter which variable is on the left hand side of the equation. In case convergence problems are encountered by matrix inversion, one can pass a higher tolerance level via "tol=..." to the solve()-function.

Value

An object of class ca.po.

Author(s)

Bernhard Pfaff

References

Phillips, P.C.B. and Ouliaris, S. (1990), Asymptotic Properties of Residual Based Tests for Cointegration, Econometrica, Vol. 58, No. 1, 165–193.

See Also

ca.po-class

Examples

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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)

Example output

######################################## 
# Phillips and 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 
-0.57878 -0.26119 -0.00787  0.20350  1.06522 

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:
                  10pct    5pct    1pct
critical values 62.1436 71.2751 89.6679

urca documentation built on May 31, 2017, 2:41 a.m.

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