Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
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)
``` |

`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 |

`a0` |
Constant term of AR(1) series |

`a1` |
Linear term of AR(1) series (e.g. coefficient of mean reversion).
For the |

`trend` |
Trend parameter. This may either
be a scalar or it may be a vector of length |

`n` |
Length of AR(1) series.
For the |

`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 |

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`

.

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.

Matthew Clegg [email protected]

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.

`adf.test`

`pp.test`

`bvr.test`

`pgff.test`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
# 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)
``` |

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