GMM estimation and asymptotic properties in periodic GARCH(1, 1) models

Lescheb Ines ()
Additional contact information
Lescheb Ines: MAM Laboratory, Department of Mathematics, Freres Mentouri Constantine 1 University, 25000 Constantine, Algeria

Monte Carlo Methods and Applications, 2025, vol. 31, issue 4, 371-380

Abstract: In this paper, we study the class of first order Periodic Generalized Autoregressive Conditional heteroscedasticity processes ( PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} for short) in which the parameters in the volatility process are allowed to switch between different regimes. First, we establish necessary and sufficient conditions for a PGARCH ⁢ ( 1 , 1 ) {\mathrm{PGARCH}(1,1)} process to have a unique stationary solution (in periodic sense) and for the existence of moments of any order. Next, we are able to estimate the unknown parameters involved in model via the so-called generalized method of moments (GMM). We construct an estimator and establish its asymptotic properties. Specifically, we demonstrate its consistency and asymptotic normality. The GMM estimator in some cases can be more efficient than the least squares estimator (LSE) and the quasi maximum likelihood estimator (QMLE). Some simulation studies are also performed to highlight the impact of our theoretical results.

Keywords: Periodic GARCH processes; periodically correlated; strictly periodically stationary; GMM estimation; QML estimation; consistency; asymptotic normality (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/mcma-2025-2019 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

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:bpj:mcmeap:v:31:y:2025:i:4:p:371-380:n:1004

Ordering information: This journal article can be ordered from
https://www.degruyte ... ournal/key/mcma/html

DOI: 10.1515/mcma-2025-2019

Access Statistics for this article

Monte Carlo Methods and Applications is currently edited by Karl K. Sabelfeld

More articles in Monte Carlo Methods and Applications from De Gruyter
Bibliographic data for series maintained by Peter Golla ().