Bernoulli

  • Bernoulli
  • Volume 15, Number 4 (2009), 1057-1081.

On approximate pseudo-maximum likelihood estimation for LARCH-processes

Jan Beran and Martin Schützner

Full-text: Open access

Abstract

Linear ARCH (LARCH) processes were introduced by Robinson [J. Econometrics 47 (1991) 67–84] to model long-range dependence in volatility and leverage. Basic theoretical properties of LARCH processes have been investigated in the recent literature. However, there is a lack of estimation methods and corresponding asymptotic theory. In this paper, we consider estimation of the dependence parameters for LARCH processes with non-summable hyperbolically decaying coefficients. Asymptotic limit theorems are derived. A central limit theorem with $\sqrt{n}$-rate of convergence holds for an approximate conditional pseudo-maximum likelihood estimator. To obtain a computable version that includes observed values only, a further approximation is required. The computable estimator is again asymptotically normal, however with a rate of convergence that is slower than $\sqrt{n}$.

Article information

Source
Bernoulli, Volume 15, Number 4 (2009), 1057-1081.

Dates
First available in Project Euclid: 8 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1262962226

Digital Object Identifier
doi:10.3150/09-BEJ189

Mathematical Reviews number (MathSciNet)
MR2597583

Zentralblatt MATH identifier
1200.62100

Keywords
asymptotic distribution LARCH process long-range dependence parametric estimation volatility

Citation

Beran, Jan; Schützner, Martin. On approximate pseudo-maximum likelihood estimation for LARCH-processes. Bernoulli 15 (2009), no. 4, 1057--1081. doi:10.3150/09-BEJ189. https://projecteuclid.org/euclid.bj/1262962226


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