Efficient parameter estimation for self-similar processes
TLDR
Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved in this paper, where the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator.Abstract:
Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by Fox and Taqqu. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.read more
Citations
More filters
Journal ArticleDOI
On the self-similar nature of Ethernet traffic (extended version)
TL;DR: It is demonstrated that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, and that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks.
Journal ArticleDOI
Fractionally integrated generalized autoregressive conditional heteroskedasticity
TL;DR: In this article, the FIGARCH (Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic) process is introduced and the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations.
Journal ArticleDOI
Long memory processes and fractional integration in econometrics
TL;DR: A survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance and some of the definitions of long memory are reviewed.
Journal ArticleDOI
Gaussian Semiparametric Estimation of Long Range Dependence
TL;DR: In this paper, the spectral density of a neighborhood of zero frequency is assumed to be a Gaussian distribution, with a variance which is not dependent on unknown parameters, and the theory covers simultaneously the cases f(A) -x oc, f (A) −+ 0, f(B) -+ 0 and f(C E (0, oc), as A -* 0.
Journal ArticleDOI
Long-range dependence in variable-bit-rate video traffic
TL;DR: It is shown that the long-range dependence property allows us to clearly distinguish between measured data and traffic generated by VBR source models currently used in the literature, and gives rise to novel and challenging problems in traffic engineering for high-speed networks.
References
More filters
Journal ArticleDOI
Fractional Brownian Motions, Fractional Noises and Applications
Book
Theory of point estimation
TL;DR: In this paper, the authors present an approach for estimating the average risk of a risk-optimal risk maximization algorithm for a set of risk-maximization objectives, including maximalaxity and admissibility.
Journal ArticleDOI
An introduction to long‐memory time series models and fractional differencing
TL;DR: Generation and estimation of these models are considered and applications on generated and real data presented, showing potentially useful long-memory forecasting properties.
Journal ArticleDOI
Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series
Robert Fox,Murad S. Taqqu +1 more
TL;DR: In this paper, a strongly dependent Gaussian sequence has a spectral density that satisfies the conditions that the spectral density is consistent and asymptotically normal under appropriate conditions, which are satisfied by fractional Gaussian noise and fractional ARMA.
Journal ArticleDOI
Some long‐run properties of geophysical records
TL;DR: By preparing this book, Chris Barton and Paul La Pointe have earned the gratitude of all geologists and students of fractals as discussed by the authors, and I continue to belong to this second group, and Chris and Paul clearly have put me in a very special debt to them.
Related Papers (5)
The estimation and application of long memory time series models
John Geweke,Susan Porter-Hudak +1 more