We discuss computational aspects of likelihood-based speci cation, estimation, inference, and forecasting of possibly nonstationary series with long memory. We use the arfima(p; d; q) model with deterministic regressors and we compare sampling characteristics of approximate and exact rst-order asymptotic methods. We extend the analysis using a higher-order asymptotic method, suggested by Cox an...

This paper evaluates linear models for predicting the Digital Unix five-second host load average from 1 to 30 seconds into the future. A detailed statistical study of a large number of long, fine grain load traces from a variety of real machines leads to consideration of the Box-Jenkins models (AR, MA, ARMA, ARIMA), and the ARFIMA models (due to selfsimilarity.) These models, as well as a simpl...

In this paper, taking about 7 years’ high-frequency data of the Shanghai Stock Exchange Composite Index (SSEC) as an example, we propose a daily volatility measure based on the multifractal spectrum of the high-frequency price variability within a trading day. An ARFIMA model is used to depict the dynamics of this multifractal volatility (MFV) measures. The one-day ahead volatility forecasting ...

In this paper we analyze the asymptotic properties of the popular distribution tail index estimator by Hill (1975) for dependent, heterogeneous processes. We develop new extremal dependence measures that characterize a massive array of linear, nonlinear, and conditional volatility processes with long or short memory. We prove that the Hill estimator is weakly and uniformly weakly consistent for...

This paper draws its motivation from applications in geophysics, agricultural, and environmental sciences where empirical evidence of slow decay correlations have been found for data observed on a regular lattice. Spatial ARFIMA models represent widely used class spatial analyzing such data. Here, we consider their generalization to conditional autoregressive fractional integrated moving averag...