ca.po: Phillips & Ouliaris Cointegration Test In urca: Unit Root and Cointegration Tests for Time Series Data

Description

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

Usage

 ```1 2``` ```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`.

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.

`ca.po-class`

Examples

 ```1 2 3 4 5 6 7``` ```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.