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

On approximate pseudo-maximum likelihood estimation for LARCH-processes

Jan Beran and Martin Schützner

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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 $\sqrt{n}$.

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

First available in Project Euclid: 8 January 2010

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asymptotic distribution LARCH process long-range dependence parametric estimation volatility


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.

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