Anisotropic Scaling of Random Fields with Long-Range Dependence

10.1142/12646 ◽  
2023 ◽  
Author(s):  
Donatas Surgailis
Keyword(s):  
Long Range ◽  
Random Fields ◽  
Long Range Dependence ◽  
Anisotropic Scaling

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 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

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.

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