Next Article in Journal
Empirical Credit Risk Ratings of Individual Corporate Bonds and Derivation of Term Structures of Default Probabilities
Next Article in Special Issue
Forecasting Realized Volatility Using a Nonnegative Semiparametric Model
Previous Article in Journal
Evidence of the Environmental Kuznets Curve: Unleashing the Opportunity of Industry 4.0 in Emerging Economies
Previous Article in Special Issue
On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study
Open AccessArticle

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

1
Cambridge INET, Faculty of Economics, University of Cambridge, Cambridge CB3 9DD, UK
2
Magdalene College, University of Cambridge, Cambridge CB3 0AG, UK
3
Department of Economics, Lahore University of Management Sciences, Lahore 54000, Pakistan
4
The University of Sydney Business School, The University of Sydney, Sydney, NSW 2006, Australia
5
Trinity College, University of Cambridge, Cambridge CB2 1TQ, UK
*
Author to whom correspondence should be addressed.
J. Risk Financial Manag. 2019, 12(3), 123; https://doi.org/10.3390/jrfm12030123
Received: 13 June 2019 / Revised: 17 July 2019 / Accepted: 18 July 2019 / Published: 22 July 2019
(This article belongs to the Special Issue Financial Econometrics)
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. View Full-Text
Keywords: threshold auto-regression; Markov process; stationarity threshold auto-regression; Markov process; stationarity
Show Figures

Graphical abstract

MDPI and ACS Style

Ahmed, M.F.; Satchell, S. Some Dynamic and Steady-State Properties of Threshold Auto-Regressions with Applications to Stationarity and Local Explosivity. J. Risk Financial Manag. 2019, 12, 123.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop