We establish consistency and asymptotic normality for a weighted least squares estimate (2SWLSE) of a threshold power ARCH process in both stationary and nonstationary environments. For models with heavy tail innovations, the 2SWLSE is more efficient than the quasi-maximum likelihood estimate.

This article deals with linear prediction in large dimensions. One obtains various explicit forms of the best linear predictor in a Hilbert space. The difficulty comes from the fact that the associated linear operator is, in general, not continuous. Applications to ARMAH processes, models with...

In this paper, we show that central order statistics from strictly stationary and ergodic sequences are strongly consistent estimators of population quantiles provided that the quantiles are unique. We generalize this result to strictly stationary but not necessarily ergodic sequences. We also...

The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall et al. (1998) [11] on functionals of Gaussian processes and Nordman and Lahiri (2005) [16] on linear processes. In particular, we allow nonlinear transforms of linear...