Phillips and Ouliaris Cointegration Test

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

Usage

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.

References

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

Author

Bernhard Pfaff

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 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
#>