On Semiparametric Testing of I(d) by FEXP Models

Abstract

To statistically test the assumption that a scalar-valued process is I(d), this article proposes a test statistic based on a broadband semiparametric method by use of fractional exponential (FEXP) models. The test is semiparametric in terms of flexibility in modeling spectral density. We establish the asymptotic behavior and report finite-sample performance by a Monte Carlo study.

Keywords:

• Fractional exponential models
• I(d) processes
• Semiparametric testing

Mathematics Subject Classification:

• 62M10
• 62G10

Acknowledgments

The author is grateful to the anonymous referee for the useful comments. He would also like to thank Yasumasa Matsuda for many helpful discussions on an earlier version. This work was partially supported by JSPS Grants-in-Aid for Young Scientist (B).