Central limit theorems for power variation of Gaussian integral processes with jumps

被引：0
作者：
GuangYing Liu
JiaShan Tang
XinSheng Zhang
机构：
[1] Nanjing Audit University,Department of Mathematics and Statistics
[2] Nanjing University of Posts and Telecommunications,College of Science
[3] Fudan University,Department of Statistics, School of Management
来源：
Science China Mathematics | 2014年 / 57卷
关键词：
realized power variation; long memory; jump process; central limit theorem; high frequency; 60F05; 60G99;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper presents limit theorems for realized power variation of processes of the form Xt = ∫0tφsdGs + ξt as the sampling frequency within a fixed interval increases to infinity. Here G is a Gaussian process with stationary increments, ξ is a purely non-Gaussian Lévy process independent from G, and φ is a stochastic process ensuring that the integral is well defined as a pathwise Riemann-Stieltjes integral. We obtain the central limit theorems for the case that both the continuous term and the jump term are presented simultaneously in the law of large numbers.
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页码：1671 / 1685
页数：14
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  • [1] Aït-Sahalia Y(2009)Estimating the degree of activity of jumps in high frequency data Ann Statist 37 2202-2244
  • [2] Jacod J(2009)Testing for jumps in a discretely observed process Ann Statist 37 184-222
  • [3] Aït-Sahalia Y(2010)Is Brownian motion necessary to model high-frequency data? Ann Statist 38 3093-3128
  • [4] Jacod J(2009)Power variation for Gaussian processes with stationary increments Stoch Proc Appl 119 1845-1865
  • [5] Aït-Sahalia Y(2009)Bipower variation for Gaussian processes with stationary increments J Appl Probab 46 132-150
  • [6] Jacod J(2002)Econometric analysis of realized volatility and its use in estimating stochastic volatility models J Roy Statist Soc Ser B 64 253-280
  • [7] Barndorff-Nielsen O E(2004)Power and bipower variation with stochastic volatility and jumps (with discussion) J Financial Econometrics 2 1-48
  • [8] Corcuera J M(2006)Econometrics of testing for jumps in financial economics using bipower variation J Financial Econometrics 4 1-30
  • [9] Podolskij M(2003)Arbitrage in fractional Brownian motion models Finance Stoch 7 533-553
  • [10] Barndorff-Nielsen O E(2006)Power variation of some integral fractional processes Bernoulli 12 713-735
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