Bernoulli

  • Bernoulli
  • Volume 13, Number 2 (2007), 389-422.

A recursive online algorithm for the estimation of time-varying ARCH parameters

Rainer Dahlhaus and Suhasini Subba Rao

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Abstract

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t−1$ with observations about the time point $t$ to yield an estimator of the parameter at time point $t$. The sampling properties of this estimator are studied in a non-stationary context – in particular, asymptotic normality and an expression for the bias due to non-stationarity are established. By running two recursive online algorithms in parallel with different step sizes and taking a linear combination of the estimators, the rate of convergence can be improved for parameter curves from Hölder classes of order between 1 and 2.

Article information

Source
Bernoulli, Volume 13, Number 2 (2007), 389-422.

Dates
First available in Project Euclid: 18 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1179498754

Digital Object Identifier
doi:10.3150/07-BEJ5009

Mathematical Reviews number (MathSciNet)
MR2331257

Zentralblatt MATH identifier
1127.62078

Keywords
Locally stationary recursive online algorithms time-varying ARCH process

Citation

Dahlhaus, Rainer; Subba Rao, Suhasini. A recursive online algorithm for the estimation of time-varying ARCH parameters. Bernoulli 13 (2007), no. 2, 389--422. doi:10.3150/07-BEJ5009. https://projecteuclid.org/euclid.bj/1179498754


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