egcm (version 1.0.8)

pgff.test: Unit root test of Pantula, Gonzales-Farias and Fuller

Description

Unit root test based upon the weighted symmetric estimator of Pantula, Gonzales-Farias and Fuller

Usage

pgff.test(Y, detrend = FALSE)
pgff_rho_ws(Y, detrend = FALSE)

Arguments

Y

A vector or zoo-vector

detrend

A boolean, which if TRUE, indicates that the test should be performed after removing a linear trend from Y

Value

pgff_rho_ws returns the value $rho_ws$ of the weighted symmetric estimator.pgff.test returns a list with class "htest" containing the following components:

statistic

the value of the test statistic.

parameter

the truncation lag parameter.

p.value

the p-value of the test.

method

a character string indicating what type of test was performed.

data.name

a character string giving the name of the data.

Details

The weighted symmetric estimator $rho_ws$ of Pantula, Gonzales-Farias and Fuller is given as follows: $$\hat{\rho}_{WS}=\frac{\sum_{t=2}^n Y_{t-1} Y_t}{% \sum_{t=2}^{n-1} Y_t^2 + n^{-1} \sum_{t=1}^n Y_t^2}$$

where $n$ is the length of the sequence Y.

The authors give an associated pivotal statistic and derive the limiting distribution for it, however the approach taken in this implementation was simply to determine the distribution of $rho_ws$ through simulation. Table lookup is used to determine the p-value associated with a given value of the statistic.

If detrend=TRUE, then a linear trend is removed from the data prior to computing the estimator $rho_ws$. A separate table has been computed of the distribution of values of $rho_ws$ after detrending.

This unit root test is intended to identify autoregressive sequences of order one. However, the authors state that, "A Monte Carlo study indicates that the weighted symmetric estimator performs well in second order processes."

References

Pantula, S. G., Gonzalez-Farias, G., and Fuller, W. A. (1994). A comparison of unit-root test criteria. Journal of Business & Economic Statistics, 12(4), 449-459.

See Also

adf.test egcm

Examples

# The following should produce a low p-value
pgff_rho_ws(rnorm(100))
pgff.test(rnorm(100))

# The following should produce a high p-value
pgff_rho_ws(cumsum(rnorm(100)))
pgff.test(cumsum(rnorm(100)))

# Test with an autoregressive sequence where rho = 0.8
pgff.test(rar1(100, a1=0.8))

# If there is a linear trend, pgff.test with detrend=FALSE
# is likely to find a unit root when there is none:
pgff.test(1:100 + rnorm(100))
pgff.test(1:100 + rnorm(100), detrend=TRUE)

# Display the power of the test for various values of rho and n:
pgff_power(a1=0.8, n=100, nrep=100)
pgff_power(a1=0.9, n=250, nrep=100)
pgff_power(a1=0.95, n=250, nrep=100)

# This is to be compared to the power of the adf.test at this level:
adf_power(a1=0.8, n=100, nrep=100)
adf_power(a1=0.9, n=250, nrep=100)
adf_power(a1=0.95, n=250, nrep=100)