egcm (version 1.0.8)

ur_power: Power assessment for unit root tests

Description

A collection of functions designed to assist in determining the power of various unit root tests

Usage

ur_power (ur_test, a0 = 0, a1 = 0.95, trend=0, n = 250,  nrep = 10000, p.value = 0.05, ...)
adf_power (a0=0, a1=0.95, trend=0, n=250,  nrep=10000, p.value=0.05, k=1)
bvr_power (a0=0, a1=0.95, trend=0, n=250,  nrep=10000, p.value=0.05, detrend=FALSE)
pgff_power (a0=0, a1=0.95, trend=0, n=250,  nrep=10000, p.value=0.05, detrend=FALSE)
ur_power_table (ur_test, nrep=1000, p.value=0.05, a1=c(0.995, 0.99, 0.98, 0.97, 0.96, 0.95), trend=0, n=c(100, 250, 500, 750, 1000, 1250), ...)
adf_power_table (nrep=1000, p.value=0.05, a1=c(0.995, 0.99, 0.98, 0.97, 0.96, 0.95), trend=0, n=c(250, 500, 750, 1000, 1250), k=1)
bvr_power_table (nrep=1000, p.value=0.05, a1=c(0.995, 0.99, 0.98, 0.97, 0.96, 0.95), trend=0, n=c(100, 250, 500, 750, 1000, 1250), detrend=FALSE)     
pgff_power_table (nrep=1000, p.value=0.05, a1=c(0.995, 0.99, 0.98, 0.97, 0.96, 0.95), trend=0, n=c(100, 250, 500, 750, 1000, 1250), detrend=FALSE)

Arguments

ur_test

A function that performs a unit root test. It should accept an argument consisting of a vector of real numbers, and it should return an object with the p-value stored in the field p.value. Example functions that satisfy this criterion include adf.test, pp.test, pgff.test and bvr.test

a0

Constant term of AR(1) series

a1

Linear term of AR(1) series (e.g. coefficient of mean reversion). For the *_power_table variants, this may be a vector of numbers, representing different values of the linear term that should be tried.

trend

Trend parameter. This may either be a scalar or it may be a vector of length nrep. In the latter case, each replication of the test is performed with a different value from trend.

n

Length of AR(1) series. For the *_power_table variants, this may be a vector of numbers, representing different sequence lengths that should be tried.

nrep

Number of repetitions to perform

p.value

p-value used as cutoff point for rejecting the null hypothesis

detrend

A boolean which, if TRUE, indicates that linear trends should be removed from the AR(1) series prior to performing the unit root test.

k

Number of lags to consider in Dickey-Fuller test

...

Additional arguments to be passed to the unit root test ur_test.

Value

For the *_power functions, returns the frequency of rejections of the null hypothesis.For the *_power_table functions, returns a data.frame. Each column corresponds to a value of the mean reversion coefficient given in the vector a1, and each row corresponds to a sample length given in the vector n. An entry in the table records the frequency of rejections of the null hypothesis for the given sample length and coefficient of mean reversion.

Details

The purpose of this family of functions is to provide a means for investigating the power of various unit root tests. The power of a statistical test is the probability that it will reject the null hypothesis when the null hypothesis is false.

For unit root tests, a common practice for assessing power is to randomly generate AR(1) sequences of a fixed length and with a fixed coefficient of mean reversion, and to quantify the power in terms of these two parameters. That is the approach taken here.

The *_power functions generate nrep random AR(1) sequences of length n having the parameters a0 and a1. For each such sequence, the unit root test is performed and a check is made to see if the null hypothesis is rejected at the level given by p.value. The frequency of rejections is then reported.

The *_power_table functions generate a table of powers for various choices of n and a1. These functions can take quite a while to run.

adf_power and adf_power_table report the power of the augmented Dickey-Fuller test as implemented in adf.test. bvr_power and bvr_power_table report the power of Breitung's variance ratio as implemented in bvr.test. pgff_power and pgff_power_table report the power of the weighted symmetric estimator of Pantula, Gonzalez-Farias and Fuller as implemented in pgff.test.

References

Breitung, J. (2002). Nonparametric tests for unit roots and cointegration. Journal of econometrics, 108(2), 343-363.

Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American statistical association, 74(366a), 427-431. 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 pp.test bvr.test pgff.test

Examples

# The following examples may take a long time to run
    
# Compare the power of various unit root tests for specific
# parameter values:
# adf_power(a1=0.9, n=125, p.value=0.1)
# bvr_power(a1=0.9, n=125, p.value=0.1)
# pgff_power(a1=0.9, n=125, p.value=0.1)

# library(tseries)
# ur_power(pp.test, a1=0.9, n=125, p.value=0.1)

# The following illustrates the importance of de-trending
# pgff_power(a1=0.9, n=125, p.value=0.1, trend=10)
# pgff_power(a1=0.9, n=125, p.value=0.1, trend=10, detrend=TRUE)

# Generate tables comparing the powers of various unit root tests:
# adf_power_table()
# bvr_power_table()
# pgff_power_table()
# ur_power_table(pp.test)