## The Annals of Statistics

### Statistical inference for time-varying ARCH processes

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 34, Number 3 (2006), 1075-1114.

Dates
First available in Project Euclid: 10 July 2006

https://projecteuclid.org/euclid.aos/1152540743

Digital Object Identifier
doi:10.1214/009053606000000227

Mathematical Reviews number (MathSciNet)
MR2278352

Zentralblatt MATH identifier
1113.62099

Subjects
Secondary: 62F10: Point estimation

#### Citation

Dahlhaus, Rainer; Subba Rao, Suhasini. Statistical inference for time-varying ARCH processes. Ann. Statist. 34 (2006), no. 3, 1075--1114. doi:10.1214/009053606000000227. https://projecteuclid.org/euclid.aos/1152540743

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