.fracdist {fracdist}

Numerical CDFs for Fractional Unit Root and Cointegration Tests

Description

A package for calculating numerical distribution functions of fractional unit root and cointegration test statistics. The included functions calculate critical values and P-values used in unit root tests, cointegration tests, and rank tests in the Fractionally Cointegrated Vector Autoregression (FCVAR) model (see Johansen and Nielsen, 2012).

Details

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 cointegrating 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.

Value

Returns NULL. Object included for description only.

References

James G. MacKinnon and Morten Ørregaard Nielsen, "Numerical Distribution Functions of Fractional Unit Root and Cointegration 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 cointegrated vector autoregressive model," Econometrica 80, pp.2667-2732.