ur_power | R Documentation |

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

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 matthewcleggphd@gmail.com

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`

# 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)

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.