A Permutation Test for Unit Root in an Autoregressive Model

Jiexiang Li; Lanh Tran; Sa-aat Niwitpong

doi:10.4236/am.2013.412221

Home > Journals > Physics & Mathematics > AM

Applied Mathematics > Vol.4 No.12, December 2013

A Permutation Test for Unit Root in an Autoregressive Model ()

Jiexiang Li, Lanh Tran, Sa-aat Niwitpong

Department of Applied Statistics, King Mongkut’s University of Technology, Bangkok, Thailand.
Department of Mathematics, College of Charleston, Charleston, USA.
Department of Statistics, Indiana University, Bloomington, USA.

DOI: 10.4236/am.2013.412221 PDF HTML 3,067 Downloads 4,386 Views Citations

Abstract

A permutation test (based on a finite random sample of permutations) for unit root in an autoregressive process is considered. The test can easily be carried out in practice and the proposed permutation test is neither limited to large sample sizes nor normal white noises. Simulations show that the power of the permutation test is reasonable when sample sizes are small or when the white noises have a heavy tailed distribution. The test is shown to be consistent.

Keywords

Permutation Test; Autoregressive; Nonstationary

Share and Cite:

Li, J. , Tran, L. and Niwitpong, S. (2013) A Permutation Test for Unit Root in an Autoregressive Model. Applied Mathematics, 4, 1629-1634. doi: 10.4236/am.2013.412221.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	W. A. Fuller, “Introduction to Statistical Times Series,” John Wiley & Sons, New York, 1976.
[2]	D. A. Dickey, “Estimation and Hypothesis Testing in Nonstationary Time Series,” Ph.D. Dissertation, Iowa State University, Ames, 1976.
[3]	N. H. Chan and L. T. Tran, “Nonparametric Tests for Serial Dependence,” Journal of Time Series Analysis, Vol. 13, No. 1, 1992, pp. 19-28. http://dx.doi.org/10.1111/j.1467-9892.1992.tb00092.x
[4]	H. J. Skaug and D. Dad Tjóstheim, “A Nonparametric Test of Serial Independence Based on the Empirical Distribution Function. Consistent Nonparametric Multiple Regression: The Fixed Design Case,” Biometrika, Vol. 3, 1988, pp. 591-602.
[5]	J. P. Gould and C. R. Nelson, “The Stochastic Structure of the Velocity of Money,” The American Economic Review, Vol. 64, No. 3, 1974, pp. 405-417.
[6]	M. Friedman and A. J. Schwartz, “A Monetary History of the United States 1867-1960,” Princeton University Press, Princeton, 1963.