scholarly journals Generalised spectral analysis of fractional random fields

1997 ◽  
Vol 62 (1) ◽  
pp. 64-83
Author(s):  
V. V. Anh ◽  
K. E. Lunney
Keyword(s):  
Spectral Analysis ◽  
Spectral Density ◽  
Long Range ◽  
Random Fields ◽  
Spectral Decomposition ◽  
Covariance Function ◽  
Long Range Dependence ◽  
Type Condition ◽  
Fractal Index ◽  
Fractal Characteristics

AbstractThis paper considers a large class of non-stationary random fields which have fractal characteristics and may exhibit long-range dependence. Its motivation comes from a Lipschitz-Holder-type condition in the spectral domain.The paper develops a spectral theory for the random fields, including a spectral decomposition, a covariance representation and a fractal index. From the covariance representation, the covariance function and spectral density of these fields are defined. These concepts are useful in multiscaling analysis of random fields with long-range dependence.

scholarly journals Non-Parametric Spectral Density Estimation Under Long-Range Dependence

2018 ◽  
Vol 39 (3) ◽  
pp. 380-401 ◽  
Author(s):  
Young Min Kim ◽  
Soumendra N. Lahiri ◽  
Daniel J. Nordman
Keyword(s):  
Spectral Density ◽  
Density Estimation ◽  
Long Range ◽  
Long Range Dependence ◽  
Spectral Density Estimation ◽  
Non Parametric

scholarly journals Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence

2004 ◽  
Vol 41 (A) ◽  
pp. 35-53 ◽  
Author(s):  
V. V. Anh ◽  
N. N. Leonenko ◽  
L. M. Sakhno
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Spectral Estimation ◽  
Kernel Estimation ◽  
Mathematical Finance ◽  
Higher Order ◽  
Long Range Dependence ◽  
Type Method ◽  
Minimum Contrast ◽  
Consistency And Asymptotic Normality

This paper provides a quasi-likelihood or minimum-contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general kth order and allows for possible long-range dependence in the random fields. To avoid bias due to edge effects, data tapering is incorporated into the method. The suggested minimum contrast functional is linear with respect to the periodogram of kth order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretization is not required in the estimation of continuously observed random fields. The consistency and asymptotic normality of the resulting estimators are established. Illustrative applications of the method to some problems in mathematical finance and signal detection are given.

Possible long-range dependence in fractional random fields

1999 ◽  
Vol 80 (1-2) ◽  
pp. 95-110 ◽  
Author(s):  
V.V. Anh ◽  
J.M. Angulo ◽  
M.D. Ruiz-Medina
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Long Range Dependence

On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

2007 ◽  
Vol 44 (02) ◽  
pp. 379-392
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Closed Form ◽  
Long Range ◽  
Covariance Function ◽  
Queueing System ◽  
Regenerative Process ◽  
Long Range Dependence ◽  
Exact Asymptotics ◽  
Regenerative Processes ◽  
Service Times ◽  
Heavy Tailed

In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

scholarly journals Scaling transition for nonlinear random fields with long-range dependence

2017 ◽  
Vol 127 (8) ◽  
pp. 2751-2779 ◽  
Author(s):  
Vytautė Pilipauskaitė ◽  
Donatas Surgailis
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Long Range Dependence

scholarly journals Quasi-likelihood-based higher-order spectral estimation of random fields with possible long-range dependence

2004 ◽  
Vol 41 (A) ◽  
pp. 35-53
Author(s):  
V. V. Anh ◽  
N. N. Leonenko ◽  
L. M. Sakhno
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Spectral Estimation ◽  
Kernel Estimation ◽  
Mathematical Finance ◽  
Higher Order ◽  
Long Range Dependence ◽  
Type Method ◽  
Minimum Contrast ◽  
Consistency And Asymptotic Normality

This paper provides a quasi-likelihood or minimum-contrast-type method for the parameter estimation of random fields in the frequency domain based on higher-order information. The estimation technique uses the spectral density of the general kth order and allows for possible long-range dependence in the random fields. To avoid bias due to edge effects, data tapering is incorporated into the method. The suggested minimum contrast functional is linear with respect to the periodogram of kth order, hence kernel estimation for the spectral densities is not needed. Furthermore, discretization is not required in the estimation of continuously observed random fields. The consistency and asymptotic normality of the resulting estimators are established. Illustrative applications of the method to some problems in mathematical finance and signal detection are given.

Sign in / Sign up

Export Citation Format

Share Document