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The multi-scale high-order statistical moments of financial time series

Author

Listed:
  • Jiang, Jun
  • Shang, Pengjian
  • Zhang, Zuoquan
  • Li, Xuemei

Abstract

A new high-order statistical moment based on multi-scale (MSHOM) is proposed for researching traditional statistics in this paper. In addition, the indispensable theoretical basis and derivation are illustrated in detail. With the help of three simulated time series, two kinds of situations of MSHOM analysis are mainly discussed in this work. One is accomplished by Gaussian white noise (GWN) and the other is fulfilled with Logistic map and autoregressive fractionally integrated moving-average (ARFIMA). Due to the insufficient performance of MSHOM, we propose an improved MSHOM, which is called MSHOM with control (C-MSHOM). Meanwhile, its performance is tested by the data of US and Chinese stock markets. However, C-MSHOM also brings an extra preprocess stage of data and the uncertainty of selection. To solve these problems, a more generic method, that is, generalized multi-scale high-order moments (G-MSHOM) is given in this paper.

Suggested Citation

  • Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2018. "The multi-scale high-order statistical moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 474-488.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:474-488
    DOI: 10.1016/j.physa.2018.08.101
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    References listed on IDEAS

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    1. Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2017. "Permutation entropy analysis based on Gini–Simpson index for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 273-283.
    2. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
    3. Yousry Abdelkader, 2004. "Computing the moments of order statistics from nonidentically distributed Erlang variables," Statistical Papers, Springer, vol. 45(4), pages 563-570, October.
    4. Bhardwaj, Geetesh & Swanson, Norman R., 2006. "An empirical investigation of the usefulness of ARFIMA models for predicting macroeconomic and financial time series," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 539-578.
    5. Lapan, Harvey E. & Hennessy, David A., 2008. "Statistical moments analysis of production and welfare in multi-product Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 26(2), pages 598-606, March.
    6. Akgiray, Vedat, 1989. "Conditional Heteroscedasticity in Time Series of Stock Returns: Evidence and Forecasts," The Journal of Business, University of Chicago Press, vol. 62(1), pages 55-80, January.
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    Cited by:

    1. Hong-Jiang Wu & Ying-Ying Zhang & Han-Yu Li, 2023. "Expectation identities from integration by parts for univariate continuous random variables with applications to high-order moments," Statistical Papers, Springer, vol. 64(2), pages 477-496, April.

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