Statistical Inference of Spot Correlation and Spot Market Beta under Infinite Variation Jumps*

2020 ◽  
Author(s):  
Qiang Liu ◽  
Zhi Liu
Keyword(s):  
Statistical Inference ◽  
High Frequency ◽  
Order Approximation ◽  
Estimation Procedure ◽  
Spot Market ◽  
Jump Processes ◽  
Empirical Characteristic Function ◽  
Finite Sample ◽  
Market Beta ◽  
The Individual

Abstract Empirical evidence has revealed that the jumps in financial markets appear to be very frequent. This study considers the statistical inference of the spot correlation and the spot market beta between two different assets using high-frequency data, in a setting where both the cojumps and the individual jumps in the underlying driving processes could be of infinite variation. Starting from the estimation of the spot covariance, we propose consistent estimators of the spot correlation and the spot market beta when the jump processes involved are general semimartingales. The second-order approximation for the estimators, namely, the central limit theorems, is established under the assumption that the jumps around zero are of stable Lévy type. Our estimation procedure is based on the empirical characteristic function of the increments of the processes and the application of the polarization identity; the bias terms stemming from the jumps are removed iteratively. The finite sample performances of the proposed estimators and other existing estimators are assessed and compared by using datasets simulated from various models. Our estimators are also applied to some real high-frequency financial datasets.

scholarly journals ESTIMATION OF INTEGRATED COVARIANCES IN THE SIMULTANEOUS PRESENCE OF NONSYNCHRONICITY, MICROSTRUCTURE NOISE AND JUMPS

2015 ◽  
Vol 32 (3) ◽  
pp. 533-611 ◽  
Author(s):  
Yuta Koike
Keyword(s):  
High Frequency ◽  
Monte Carlo Study ◽  
Jump Processes ◽  
Observation Data ◽  
Observation Error ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Sampling Schemes ◽  
Integrated Covariance ◽  
Asymptotic Mixed Normality

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a high frequency. This new estimator, which we call the pre-averaged truncated Hayashi–Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data are polluted by some noise. We also show the asymptotic mixed normality of this estimator under some mild conditions allowing infinite activity jump processes with finite variations, some dependency between the sampling times and the observed processes as well as a kind of endogenous observation error. We examine the finite sample performance of this estimator using a Monte Carlo study and we apply our estimators to empirical data, highlighting the importance of accounting for jumps even in an ultra-high frequency framework.

scholarly journals Terminal-Dependent Statistical Inference for the Integral Form of FBSDE

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Qi Zhang
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Statistical Inference ◽  
Backward Stochastic Differential Equation ◽  
Integral Form ◽  
Estimation Procedure ◽  
Terminal Condition ◽  
Finite Sample ◽  
Inference Procedure ◽  
Key Factor

Backward Stochastic Differential Equation (BSDE) has been well studied and widely applied. The main difference from the Original Stochastic Differential Equation (OSDE) is that the BSDE is designed to depend on a terminal condition, which is a key factor in some financial and ecological circumstances. However, to the best of knowledge, the terminal-dependent statistical inference for such a model has not been explored in the existing literature. This paper is concerned with the statistical inference for the integral form of Forward-Backward Stochastic Differential Equation (FBSDE). The reason why I use its integral form rather than the differential form is that the newly proposed inference procedure inherits the terminal-dependent characteristic. In this paper the FBSDE is first rewritten as a regression version, and then a semiparametric estimation procedure is proposed. Because of the integral form, the newly proposed regression version is more complex than the classical one, and thus the inference methods are somewhat different from those designed for the OSDE. Even so, the statistical properties of the new method are similar to the classical ones. Simulations are conducted to demonstrate finite sample behaviors of the proposed estimators.

High-Frequency Financial Econometrics

2014 ◽  
Author(s):  
Yacine Aït-Sahalia ◽  
Jean Jacod
Keyword(s):  
High Frequency ◽  
Practical Importance ◽  
Financial Econometrics ◽  
Trading Strategies ◽  
Financial Data ◽  
Jump Processes ◽  
High Frequency Trading ◽  
Microstructure Noise ◽  
Econometric Methods ◽  
Mathematical Foundations

High-frequency trading is an algorithm-based computerized trading practice that allows firms to trade stocks in milliseconds. Over the last fifteen years, the use of statistical and econometric methods for analyzing high-frequency financial data has grown exponentially. This growth has been driven by the increasing availability of such data, the technological advancements that make high-frequency trading strategies possible, and the need of practitioners to analyze these data. This comprehensive book introduces readers to these emerging methods and tools of analysis. The book covers the mathematical foundations of stochastic processes, describes the primary characteristics of high-frequency financial data, and presents the asymptotic concepts that their analysis relies on. It also deals with estimation of the volatility portion of the model, including methods that are robust to market microstructure noise, and address estimation and testing questions involving the jump part of the model. As the book demonstrates, the practical importance and relevance of jumps in financial data are universally recognized, but only recently have econometric methods become available to rigorously analyze jump processes. The book approaches high-frequency econometrics with a distinct focus on the financial side of matters while maintaining technical rigor, which makes this book invaluable to researchers and practitioners alike.

Incorporating predictions into an annual forest inventory

1996 ◽  
Vol 26 (9) ◽  
pp. 1709-1713 ◽  
Author(s):  
Paul C. Van Deusen
Keyword(s):  
Forest Inventory ◽  
Variance Components ◽  
Growth Modeling ◽  
Estimation Procedure ◽  
Regression Estimator ◽  
Forest Types ◽  
Model Estimate ◽  
Individual Tree ◽  
Time Period ◽  
The Individual

Growth modeling of forests at the individual tree and stand levels is a highly refined procedure for many forest types. A method to incorporate predictions from such models into a forest inventory system is developed. Variance components from the actual measurements and from the predicted measurements are used to estimate the variance of the combined predicted value. The only assumption required to justify this method is that the model estimate has a bias that does not change from one time period to the next. The estimation procedure proposed here can also incorporate remotely sensed information via a regression estimator.

scholarly journals An autoregressive model for irregular time series of variable stars

2016 ◽  
Vol 12 (S325) ◽  
pp. 259-262
Author(s):  
Susana Eyheramendy ◽  
Felipe Elorrieta ◽  
Wilfredo Palma
Keyword(s):  
Time Series ◽  
Gravitational Lensing ◽  
Autoregressive Model ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Variable Stars ◽  
Light Curves ◽  
Finite Sample ◽  
Harmonic Model ◽  
Dependency Structure

AbstractThis paper discusses an autoregressive model for the analysis of irregularly observed time series. The properties of this model are studied and a maximum likelihood estimation procedure is proposed. The finite sample performance of this estimator is assessed by Monte Carlo simulations, showing accurate estimators. We implement this model to the residuals after fitting an harmonic model to light-curves from periodic variable stars from the Optical Gravitational Lensing Experiment (OGLE) and Hipparcos surveys, showing that the model can identify time dependency structure that remains in the residuals when, for example, the period of the light-curves was not properly estimated.

Imputed Estimation For Varying Coefficient Models with Missing Covariates

2013 ◽  
Vol 787 ◽  
pp. 1089-1092
Author(s):  
Pei Xin Zhao
Keyword(s):  
Missing Data ◽  
Estimation Procedure ◽  
Estimating Equation ◽  
Equation Method ◽  
Missing Covariates ◽  
Varying Coefficient Models ◽  
Finite Sample ◽  
Varying Coefficient

By using the imputation-based estimating equation method, an imputed estimation procedure for the coefficient functions is proposed. The proposed procedure can attenuate the effect of the missing data, and performs well for the finite sample.

Abstract P502: Abnormal Myocyte Calcium Dynamics And The Resultant Contraction Band Formation Of The Rat Heart Under Irreversible Injury By Membrane Permeabilization

2021 ◽  
Vol 129 (Suppl_1) ◽  
Author(s):  
Yuma Morishita ◽  
Shoko Tamura ◽  
Kentaro Mochizuki ◽  
Yoshinori Harada ◽  
Hideo Tanaka
Keyword(s):  
Fluorescence Intensity ◽  
High Frequency ◽  
Time Course ◽  
Morphological Changes ◽  
Confocal Imaging ◽  
Band Formation ◽  
Contraction Band Necrosis ◽  
Scanning Confocal Microscopy ◽  
The Individual ◽  
Contraction Band

Ca 2+ overload is a cardinal feature of cardiomyocyte injury, and its progression to irreversible state leads to cell death. However, unknowns are the precise spatiotemporal changes in the myocyte Ca 2+ dynamics and the relevant cell morphology of irreversibly injured hearts. On the hypothesis that myocytes exhibit high-frequency Ca 2+ waves and contraction band necrosis in saponin-permeabilized injured heart, we observed changes in the Ca 2+ dynamics and the relevant morphological changes in the subepicardial myocardium of the Fluo4-loaded rat hearts (n = 14) by rapid-scanning confocal microscopy (100 frames/s) under Langendorff perfusion with 0.3 mM Ca 2+ -Tyrode solution including 0.4 % saponin at 30°C. Also performed was confocal imaging of tetramethylrhodamine methyl ester (TMRM) fluorescence of the myocardium. Under quasi-quiescence of the heart after dissection of the SA node, individual myocytes barely exhibited spontaneous Ca 2+ waves, whereas after commencement of saponin perfusion high-frequency (118 ± 9.7 /min/cell, mean ± SEM) Ca 2+ waves (hereafter, “agonal waves”) emerged within 1 min, showing asynchronous, oscillatory contractions in the individual myocytes with a V prop of 124 ± 2.5 μm/s (n = 60). Subsequently, the waves gradually decreased in frequency with concomitant slowing of its decay time course, and eventually, disappeared in 6 min; myocytes exhibited high, static Fluo4-fluorescence intensity. Along with the progression of Ca 2+ overload by saponin, the TMRM fluorescence intensity was discretely lost in individual myocytes. The myocytes showing the agonal waves exhibited contraction bands, i.e., band-like aggregations of the actin fibers. Under mechanical arrest of the heart by 2,3-butanedione monoxime (20 mM), saponin still induced the agonal waves with a frequency of 253 ± 10.6 /cell/min and V prop of 118 ± 2.1 μm/s (n = 60); however, contraction bands were barely seen.In conclusion, irreversible myocyte injury by saponin provoked agonal Ca 2+ waves and oscillatory contractions indicating progressive Ca 2+ overload and the following mitochondrial damage, which may provide deeper insights into understanding the mechanism of contraction band necrosis.

Individual entrenchment vs. community-wide conventionalization of contact features in L2 Basque speakers’ individual styles

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Hanna Lantto
Keyword(s):  
Individual Variation ◽  
High Frequency ◽  
Personal Experience ◽  
Language Contact ◽  
Language Attitudes ◽  
Linguistic Variation ◽  
Speech Styles ◽  
Speech Patterns ◽  
Base Language ◽  
The Individual

AbstractThis article examines individual variation of contact features in the speech patterns of four L2 Basque speakers. The individual styles are examined through the concepts of individual entrenchment and community-wide conventionalization to bridge the gap between linguistic variation and change at the individual and social levels. All the informants speak Spanish as their L1. They have acquired Basque in classroom contexts, and they belong to the same macrosociolinguistic categories. Yet their patterns of using the language contact between standard Basque, vernacular Basque dialects and Spanish as a resource in creating individual speech styles differ considerably, reflecting their language attitudes and their personal experience. Nevertheless, there are conventionalized patterns that emerge out of this diversity: All speakers use the standard Basque as the base language, and none of them adopts of vernacular variety as a whole. The Spanish resources seem to be used mainly for pragmatic and stylistic functions, whereas the features of vernacular Basque that the speakers have adopted as part of their individual styles are high frequency elements of core grammar.

scholarly journals The Atmospheric δ13C Record as Derived from 56 Pinyon Trees at 14 Sites in the Southwestern United States

Radiocarbon ◽  
1989 ◽  
Vol 31 (03) ◽  
pp. 469-474 ◽  
Author(s):  
S W Leavitt ◽  
Austin Long
Keyword(s):  
High Frequency ◽  
Ice Core ◽  
Ring Width ◽  
Ice Cores ◽  
The Other ◽  
Core Data ◽  
Single Tree ◽  
Pinyon Pine ◽  
The Individual ◽  
First Time

We have developed a master δ13C chronology from 14 pinyon pine sites in 6 states of the southwestern U S. Two of the individual isotopic chronologies, reported here for the first time, and 10 of those previously reported (Leavitt & Long, 1986; 1988) are from sites where cores from 4 trees were pooled prior to analysis, and the other 2 are merged from groups of 4 single-tree chronologies (sites) developed in an earlier phase of research (Leavitt & Long, 1985). Regressions of first differences of ring-width indices and δ13C values from each site were used to “correct” individual δ13C chronologies for climate effects which appear primarily related to high-frequency δ13C fluctuations, many of which are common among sites. These climate-corrected chronologies were normalized as deviations from their respective 1800–1849 δ13C means, and these normalized chronologies were averaged into the master. The overall δ13C drop from 1600 to the present is ca 1.2–1.4, consistent with recent ice-core data showing a drop of 1.14 ± 0.15% from 1740 to present (Friedli et al, 1986). However, the δ13C decline in the late 19th and early 20th centuries is greater in the pinyon chronology than that of the ice cores, thus supporting a greater biospheric CO2 input to the atmosphere than that indicated in the ice-core data.

scholarly journals The nuclear spin of iodine I— fine structure in the first spark spectrum

1935 ◽  
Vol 149 (867) ◽  
pp. 269-281 ◽  
Keyword(s):  
Fine Structure ◽  
High Resolution ◽  
Nuclear Spin ◽  
High Frequency ◽  
Complete Resolution ◽  
Electrodeless Discharge ◽  
A Value ◽  
Fabry Perot ◽  
Fine Structures ◽  
The Individual

In an earlier paper on the fine structures of the visible lines in the arc spectra of bromine and iodine an attempt was made to estimate the nuclear spin of iodine, and a tentative value of 9/2 was proposed. The iodine arc lines were excited by a high frequency electrodeless discharge in pure iodine vapour and examined with a silvered Fabry-perot interferometer. The fine structures in the arc lines are small, and as the patterns are highly complex and the individual components not very sharp, interpretation was difficult. It was concluded with certainty that the nuclear spin was at least equal to 5/2, but one line in particular suggested a value of 9/2. This was indefinite, and in view of the uncertainty a thorough examination of both the arc and spark spectra of iodine has been undertaken. A preliminary notice has already appeared. The first spark spectrum can be more easily studied than the arc spectrum, since the structure are on a very much bigger scale and more complete resolution can be attained. The present work is concerned with the spark lines excited in a hollow cathode discharge. Fine structures in iodine spark lines were first recorded long ago by Wood and Kimura who excited the lines in a Geissler tube and examined them with a transmission echelon. Murakawa attempted to analyse the fine structure data, but as the source and instrument employed by Wood and Kimura were not able to give the high resolution attained here, the deductions made from these data, although generally correct, are uncertain and require further examination; for many of the line structures are much more complex than as reported by these earlier observers.

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