Open Access
Translator Disclaimer
June 2006 Statistical inference for time-varying ARCH processes
Rainer Dahlhaus, Suhasini Subba Rao
Ann. Statist. 34(3): 1075-1114 (June 2006). DOI: 10.1214/009053606000000227


In this paper the class of ARCH(∞) models is generalized to the nonstationary class of ARCH(∞) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation “locally stationary ARCH(∞) process.” The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p<∞) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.


Download Citation

Rainer Dahlhaus. Suhasini Subba Rao. "Statistical inference for time-varying ARCH processes." Ann. Statist. 34 (3) 1075 - 1114, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1113.62099
MathSciNet: MR2278352
Digital Object Identifier: 10.1214/009053606000000227

Primary: 62M10
Secondary: 62F10

Keywords: Derivative process , Locally stationary , quasi-likelihood estimates , time-varying ARCH process

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
Back to Top