On approximate pseudo-maximum likelihood estimation for LARCH-processes

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 root n-rate of convergence holds for in 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 root n