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Testing long memory based on a discretely observed process

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Statistics, Nanjing Audit University, Nanjing, 210029, China

    Guang-ying Liu

  2. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Guang-ying Liu

  3. Department of Statistics, Fudan University, Shanghai, 200433, China

    Xin-sheng Zhang

  4. Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China

    Shi-bin Zhang

Authors
  1. Guang-ying Liu
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  2. Xin-sheng Zhang
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  3. Shi-bin Zhang
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Correspondence to Guang-ying Liu.

Additional information

Supported by National NSFC(11501503), Natural Science Foundation of Jiangsu Province of China (BK20131340), China Postdoctoral Science Foundation (2014M560471, 2016T90534), QingLan 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).

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Liu, Gy., Zhang, Xs. & Zhang, Sb. Testing long memory based on a discretely observed process. Appl. Math. J. Chin. Univ. 31, 253–268 (2016). https://doi.org/10.1007/s11766-016-3342-y

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  • DOI: https://doi.org/10.1007/s11766-016-3342-y

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