Estimation in threshold autoregressive models with a stationary and a unit root regime

Jiti Gao, Dag Tjøstheim and Jiying Yin

No 21/11, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: This paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models have basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is asymptotically proportional to n-1/4, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated data and a real data example.

Keywords: Autoregressive process; null-recurrent process; semiparametric model; threshold time series; unit root structure. (search for similar items in EconPapers)
JEL-codes: C14 C18 C22 (search for similar items in EconPapers)
Pages: 36 pages
Date: 2011-09
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://business.monash.edu/econometrics-and-busine ... ions/ebs/wp21-11.pdf (application/pdf)

Related works:
Journal Article: Estimation in threshold autoregressive models with a stationary and a unit root regime (2013)
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:msh:ebswps:2011-21

Ordering information: This working paper can be ordered from
http://business.mona ... -business-statistics

Access Statistics for this paper

More papers in Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics PO Box 11E, Monash University, Victoria 3800, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Professor Xibin Zhang ().