The Annals of Statistics

Statistical inference for time-varying ARCH processes

Rainer Dahlhaus and Suhasini Subba Rao

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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

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

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F10: Point estimation

Derivative process locally stationary quasi-likelihood estimates time-varying ARCH process


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

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