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 $\sqrt{n}$.
Citation
Jan Beran. Martin Schützner. "On approximate pseudo-maximum likelihood estimation for LARCH-processes." Bernoulli 15 (4) 1057 - 1081, November 2009. https://doi.org/10.3150/09-BEJ189
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