Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion

Author

Ping YU, University of Hong Kong
Peter C. B. PHILLIPS, Singapore Management UniversityFollow

Publication Type

Journal Article

Version

acceptedVersion

Publication Date

11-2018

Abstract

The asymptotic distribution of the least squares estimator in threshold regression is expressed in terms of a compound Poisson process when the threshold effect is fixed and as a functional of two-sided Brownian motion when the threshold effect shrinks to zero. This paper explains the relationship between this dual limit theory by showing how the asymptotic forms are linked in terms of joint and sequential limits. In one case, joint asymptotics apply when both the sample size diverges and the threshold effect shrinks to zero, whereas sequential asymptotics operate in the other case in which the sample size diverges first and the threshold effect shrinks subsequently. The two operations lead to the same limit distribution, thereby linking the two different cases. The proofs make use of ideas involving limit theory for sums of a random number of summands.

Keywords

Threshold regression, Sequential asymptotics, Doob's martingale inequality, Compound Poisson process, Brownian motion

Discipline

Econometrics

Research Areas

Econometrics

Publication

Economics Letters

Volume

172

First Page

123

Last Page

126

ISSN

0165-1765

Identifier

10.1016/j.econlet.2018.08.039

Publisher

Elsevier

Citation

YU, Ping and PHILLIPS, Peter C. B.. Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion. (2018). Economics Letters. 172, 123-126.
Available at: https://ink.library.smu.edu.sg/soe_research/2353

Copyright Owner and License

Authors

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Additional URL

https://doi.org/10.1016/j.econlet.2018.08.039