Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity

Muhammad Farid Ahmed and Stephen Satchell
Additional contact information
Muhammad Farid Ahmed: Cambridge INET, Faculty of Economics, University of Cambridge, Cambridge CB3 9DD, UK
Stephen Satchell: The University of Sydney Business School, The University of Sydney, Sydney, NSW 2006, Australia

JRFM, 2019, vol. 12, issue 3, 1-18

Abstract: The purpose of this paper is to investigate the dynamics and steady-state properties of threshold autoregressive models with exogenous states that follow Markovian processes. Markovian processes are widely used in applied economics although their statistical properties have not been explored in detail. We use characteristic functions to carry out the analysis, and this allows us to describe limiting distributions for processes not considered in the literature previously. We also calculate analytical expressions for some moments. Furthermore, we see that we can have locally explosive processes that are explosive in one regime whilst being strongly stationary overall. This is explored through simulation analysis, where we also show how the distribution changes when the explosive state becomes more frequent although the overall process remains stationary. In doing so, we are able to relate our analysis to asset prices which exhibit similar distributional properties.

Keywords: threshold auto-regression; Markov process; stationarity (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/1911-8074/12/3/123/pdf (application/pdf)
https://www.mdpi.com/1911-8074/12/3/123/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:12:y:2019:i:3:p:123-:d:250648

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().