Testing long memory based on a discretely observed process  

作　　者：LIU Guang-ying ZHANG Xin-sheng ZHANG Shi-bin 

机构地区：[1]Department of Statistics, Nanjing Audit University [2]School of Mathematical Sciences, Zhejiang University [3]Department of Statistics, Fudan University [4]Department of Mathematics, Shanghai Maritime University

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2016年第3期253-268,共16页高校应用数学学报（英文版）（B辑）

基　　金：Supported by National NSFC(11501503);Natural Science Foundation of Jiangsu Province of China(BK20131340);China Postdoctoral Science Foundation(2014M560471,2016T90534);Qing Lan Project of Jiangsu Province of China;Priority Academic Program Development of Jiangsu Higher Education Institutions(Applied Economics);Key Laboratory of Jiangsu Province(Financial Engineering Laboratory)

摘　　要：In this paper we consider the problem of testing long memory for a continuous time process based on high frequency data. We provide two test statistics to distinguish between a semimartingale and a fractional integral process with jumps, where the integral is driven by a fractional Brownian motion with long memory. The small-sample performances of the statistics are evidenced by means of simulation studies. The real data analysis shows that the fractional integral process with jumps can capture the long memory of some financial data.In this paper we consider the problem of testing long memory for a continuous time process based on high frequency data. We provide two test statistics to distinguish between a semimartingale and a fractional integral process with jumps, where the integral is driven by a fractional Brownian motion with long memory. The small-sample performances of the statistics are evidenced by means of simulation studies. The real data analysis shows that the fractional integral process with jumps can capture the long memory of some financial data.

关 键 词：long memory JUMP fractional Brownian motion SEMIMARTINGALE high frequency data power variation 

分 类 号：O211.6[理学—概率论与数理统计]