Phillips and Perron Unit Root Test

Performs the Phillips and Perron unit root test. Beside the Z statistics Z-alpha and Z-tau, the Z statistics for the deterministic part of the test regression are computed, too.

Usage

ur.pp(x, type = c("Z-alpha", "Z-tau"), model = c("constant", "trend"),
      lags = c("short", "long"), use.lag = NULL)

Arguments

x: Vector to be tested for a unit root.
type: Test type, either "Z-alpha" or "Z-tau".
model: Determines the deterministic part in the test regression.
lags: Lags used for correction of error term.
use.lag: Use of a different lag number, specified by the user.

Details

The function ur.pp() computes the Phillips and Perron test. For correction of the error term a Bartlett window is used.

Value

An object of class ur.pp.

References

Phillips, P.C.B. and Perron, P. (1988), Testing for a unit root in time series regression, Biometrika, 75(2), 335–346.

MacKinnon, J.G. (1991), Critical Values for Cointegration Tests, Long-Run Economic Relationships, eds. R.F. Engle and C.W.J. Granger, London, Oxford, 267–276.

Download possible at: https://cowles.yale.edu/, see rubric 'Discussion Papers (CFDPs)'.

Author

Bernhard Pfaff

Examples

data(nporg)
gnp <- na.omit(nporg[, "gnp.r"])
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
#>