A Tight Lower Bound for High Frequency Moment Estimation with Small Error

Author(s):  
Yi Li ◽  
David P. Woodruff
2014 ◽  
Vol 51 (A) ◽  
pp. 161-173 ◽  
Author(s):  
Anita Behme ◽  
Claudia Klüppelberg ◽  
Kathrin Mayr

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.


2014 ◽  
Vol 10 (2) ◽  
pp. 825-841 ◽  
Author(s):  
M. Comboul ◽  
J. Emile-Geay ◽  
M. N. Evans ◽  
N. Mirnateghi ◽  
K. M. Cobb ◽  
...  

Abstract. The ability to precisely date climate proxies is central to the reconstruction of past climate variations. To a degree, all climate proxies are affected by age uncertainties, which are seldom quantified. This article proposes a probabilistic age model for proxies based on layer-counted chronologies, and explores its use for annually banded coral archives. The model considers both missing and doubly counted growth increments (represented as independent processes), accommodates various assumptions about error rates, and allows one to quantify the impact of chronological uncertainties on different diagnostics of variability. In the case of a single coral record, we find that time uncertainties primarily affect high-frequency signals but also significantly bias the estimate of decadal signals. We further explore tuning to an independent, tree-ring-based chronology as a way to identify an optimal age model. A synthetic pseudocoral network is used as testing ground to quantify uncertainties in the estimation of spatiotemporal patterns of variability. Even for small error rates, the amplitude of multidecadal variability is systematically overestimated at the expense of interannual variability (El Niño–Southern Oscillation, or ENSO, in this case), artificially flattening its spectrum at periods longer than 10 years. An optimization approach to correct chronological errors in coherent multivariate records is presented and validated in idealized cases, though it is found difficult to apply in practice due to the large number of solutions. We close with a discussion of possible extensions of this model and connections to existing strategies for modeling age uncertainties.


Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1025
Author(s):  
Laura Ciupala ◽  
Adrian Deaconu

There are various situations in which real-world problems can be modeled and solved as minimum flow problems. Sometimes, in these situations, minor data changes may occur, leading to corresponding changes of the networks in which the practical problems are modeled as flow problems, such as slight variations in capacity or lower bound. For instance, the capacity or the lower bound of an arc may increase or decrease in time, leaving one with no other choice than finding the new minimum network flow. Given both the various ways in which the networks can be changed and the high frequency of these changes, it is desirable to find as fast a computation method for minimum flow as possible. This paper is focused on the cases that concern increasing and decreasing the capacity or the lower bound of an arc. For these cases, both the minimum flow algorithms and the dynamic minimum flow algorithms that are already known are inefficient. Our incremental algorithms for determining minimum flow in the modified network are more efficient than both the above-mentioned types of algorithms. The proposed method starts from the initial network minimum flow and solves the minimum flow problem in a significantly faster way than recalculating the new network minimum flow starting from scratch.


2014 ◽  
Vol 51 (A) ◽  
pp. 161-173 ◽  
Author(s):  
Anita Behme ◽  
Claudia Klüppelberg ◽  
Kathrin Mayr

Financial data are as a rule asymmetric, although most econometric models are symmetric. This applies also to continuous-time models for high-frequency and irregularly spaced data. We discuss some asymmetric versions of the continuous-time GARCH model, concentrating then on the GJR-COGARCH model. We calculate higher-order moments and extend the first-jump approximation. These results are prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH model parameters, respectively, which we derive in detail.


2000 ◽  
Vol 639 ◽  
Author(s):  
A. R. Vasconcellos ◽  
R. Luzzi ◽  
C. G. Rodríguez ◽  
V. N. Freire ◽  
A. P. da Costa

ABSTRACTWe consider the behavior of the absorption coefficient and luminescence spectrum in the steady state when III-nitrides semiconductors (compounds GaN, AlN, and InN) are in far-fromequilibrium conditions created by an electric field. We analyze the high frequency part of the spectra obtaining a generalization of the Roosbroeck-Schockley relation, δRS(ω, EF), the ratio between the frequency dependent luminescence I(ω) and the absorption coefficient α(ω), for nonequilibrium conditions which are dependent on the electric field intensity EF. We show that the carrier's temperature within a small error is proportional to d ln[δRS(ω, EF)]/dω.


2021 ◽  
Vol 9 ◽  
Author(s):  
Hailin Du

A ruptured front obtained from high-frequency energy radiation is the key to understand the complex source. It is commonly observed that rupture fronts derived from different arrays often show some variations due to the obvious difference of the positioning accuracy of the far-field array between the azimuth and the epicentral distance. We developed a new multi-array back-projection method based on the classical back-projection method and applied the method to the 2015 MW7.8 Nepal earthquake. The back azimuth information with small error is separated from the classical back-projection results, and the azimuth intersection of multiple arrays is used to obtain more accurate spatial and temporal distribution information of the source rupture fronts.


Author(s):  
Mingyang Lu ◽  
Liming Chen ◽  
Xiaobai Meng ◽  
Ruochen Huang ◽  
Anthony Peyton ◽  
...  

Previously, various techniques have been proposed for reducing the lift-off effect on the thickness measurement of the non-magnetic films, including the peak-frequency feature and phase feature in the Dodd-Deed analytical formulation. To realise a real-time feedback response on the thickness monitoring, the phase term in the Dodd-Deeds formulation must be taken off the integration. Previous methods were based on the slow change rate of the phase term when compared to the rest of the term – the magnitude term. However, the change rate of the phase term is still considerable for a range of working frequencies. In this paper, a high-frequency feature has been found. That is, the ratio between the imaginary and real part of the phase term is proportional to the integral variable under high frequencies. Based on this proportion relationship, the phase term has been taken out; and a thickness algorithm has been proposed. By combing the measured impedance from the custom-built sensor (three coils), the thickness of the metallic film can be reconstructed. Experiments have been carried out for the verification of the proposed scenario. Results show that the thickness of the metal film can be reconstructed with a small error of less than 2 %, and immune to a reasonable range of lift-offs.


2013 ◽  
Vol 9 (5) ◽  
pp. 6077-6123 ◽  
Author(s):  
M. Comboul ◽  
J. Emile-Geay ◽  
M. N. Evans ◽  
N. Mirnateghi ◽  
K. M. Cobb ◽  
...  

Abstract. The ability to precisely date climate proxies is central to the reconstruction of past climate variations. To a degree, all climate proxies are affected by age uncertainties, which are seldom quantified. This article proposes a probabilistic age model for proxies based on layer-counted chronologies, and explores its use for annually-banded coral archives. The model considers both missing and doubly-counted growth increments (represented as independent processes), accommodates various assumptions about error rates, and allows to quantify the impact of chronological uncertainties on different diagnostics of variability. In one dimension, we find that time uncertainties primarily affect high-frequency signals but also significantly bias the estimate of decadal signals. We further explore tuning to an independent, tree-ring based chronology as a way to identify an optimal age model. In the multivariate case, a synthetic pseudocoral network is used as testing ground to quantify uncertainties in the estimation of spatiotemporal patterns of variability. Even for small error rates, the amplitude of multidecadal variability is systematically overestimated at the expense of interannual variability (ENSO, in this case), artificially flattening its spectrum at periods longer than 10 yr. An approach to correct chronological errors in coherent multivariate records is presented and validated in idealized cases, though it is found difficult to apply in practice due to the large size of the solution space. We end with a discussion of possible extensions of this model and connections to existing strategies for modeling age uncertainties.


Author(s):  
W. E. Lee ◽  
A. H. Heuer

IntroductionTraditional steatite ceramics, made by firing (vitrifying) hydrous magnesium silicate, have long been used as insulators for high frequency applications due to their excellent mechanical and electrical properties. Early x-ray and optical analysis of steatites showed that they were composed largely of protoenstatite (MgSiO3) in a glassy matrix. Recent studies of enstatite-containing glass ceramics have revived interest in the polymorphism of enstatite. Three polymorphs exist, two with orthorhombic and one with monoclinic symmetry (ortho, proto and clino enstatite, respectively). Steatite ceramics are of particular interest a they contain the normally unstable high-temperature polymorph, protoenstatite.Experimental3mm diameter discs cut from steatite rods (∼10” long and 0.5” dia.) were ground, polished, dimpled, and ion-thinned to electron transparency using 6KV Argon ions at a beam current of 1 x 10-3 A and a 12° angle of incidence. The discs were coated with carbon prior to TEM examination to minimize charging effects.


Author(s):  
G. Y. Fan ◽  
J. M. Cowley

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.


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