Numerical Distribution Functions of Fractional Unit Root and Co-Integration Tests
Numerical asymptotic distribution functions of likelihood ratio tests for fractional unit roots and co-integration rank. For these distributions, the included functions calculate critical values and P-values used in unit root tests, co-integration tests, and rank tests in the Fractionally Co-integrated Vector Autoregression (FCVAR) model.
Simple tabulation is not a feasible approach for obtaining critical values and P-values because these distributions depend on a real-valued parameter b that must be estimated. Instead, response surface regressions are used to obtain the numerical distribution functions and combined by model averaging across values taken from a series of tables. As a function of the dimension of the problem, q, and a value of the fractional integration order b, this approach provides either a set of critical values or the asymptotic P-value for any value of the likelihood ratio statistic. The P-values and critical values are calculated by interpolating from the quantiles on a grid of probabilities and values of the fractional integration order, with separate tables for a range of values of co-integrating rank.
The functions in this package are based on the functions and subroutines
in the Fortran program fracdist.f
to accompany an article by MacKinnon and Nielsen (2014).
This program is available from the archive
of the Journal of Applied Econometrics at
http://qed.econ.queensu.ca/jae/datasets/mackinnon004/.
Alternatively, a C++ implementation of this program is also available; see
https://github.com/jagerman/fracdist/blob/master/README.md
for details.
James G. MacKinnon and Morten Ørregaard Nielsen, "Numerical Distribution Functions of Fractional Unit Root and Co-integration Tests," Journal of Applied Econometrics, Vol. 29, No. 1, 2014, pp.161-171.
Johansen, S. and M. Ø. Nielsen (2012). "Likelihood inference for a fractionally co-integrated vector autoregressive model," Econometrica 80, pp.2667-2732.
Install the development version on GitHub using the devtools package:
library(devtools)
devtools::install_github("LeeMorinUCF/fracdist")
> # Calculate P-values:
> fracdist_values(iq = 1, iscon = 0, bb = 0.43, stat = 3.84)
[1] 0.05004352
> fracdist_values(iq = 1, iscon = 0, bb = 0.73, stat = 3.84)
[1] 0.0461
> # Calculate critical values:
> fracdist_values(iq = 1, iscon = 0, bb = 0.73, ipc = FALSE, clevel = 0.05)
[1] 3.7066
> fracdist_values(iq = 1, iscon = 0, bb = 0.43, ipc = FALSE, clevel = 0.05)
[1] 3.841459
> fracdist_values(iq = 1, iscon = 0, bb = 0.73, ipc = FALSE)
[1] 6.4588 3.7066 2.5927
fracdist_0.1.2:Third submission after adjustments to documentation:
fracdist_0.1.1:Second submission after adjustments to documentation:
\dontrun environment.fracdist_0.1.0:NEWS.md file to track changes to the package.There were no ERRORs or WARNINGs.
There was one NOTE:
New submission
There are currently no downstream dependencies for this package.