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Stability and lack of memory of the returns of the Hang Seng index

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  • Burnecki, Krzysztof
  • Gajda, Janusz
  • Sikora, Grzegorz

Abstract

In this paper we show that the logarithmic returns of the Hang Seng index from January 2, 1987 to November 14, 2005 statistically resemble a sequence of independent identically distributed Lévy stable random variables. This is in stark contrast to Xiu and Jin (2007) [39], where long-memory FARIMA processes with Gaussian noise were suggested as well fitted to the data. The lack of memory is checked by using Lo’s modified R/S statistic and a new method of estimation of the memory parameter d which applies the notion of empirical mean-squared displacement. In order to test stability of the data we employ several statistical tests based on the empirical distribution function. Finally, we also show that the returns possess no conditional heteroscedasticity property thus excluding the ARCH/GARCH family of processes as possible underlying models.

Suggested Citation

  • Burnecki, Krzysztof & Gajda, Janusz & Sikora, Grzegorz, 2011. "Stability and lack of memory of the returns of the Hang Seng index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3136-3146.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:18:p:3136-3146
    DOI: 10.1016/j.physa.2011.04.025
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    References listed on IDEAS

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    1. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501.
    3. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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    Citations

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    Cited by:

    1. Giuricich, Mario Nicoló & Burnecki, Krzysztof, 2019. "Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 498-513.
    2. Pablo Su'arez-Garc'ia & David G'omez-Ullate, 2012. "Scaling, stability and distribution of the high-frequency returns of the IBEX35 index," Papers 1208.0317, arXiv.org.
    3. Balcerek, Michał & Burnecki, Krzysztof, 2020. "Testing of fractional Brownian motion in a noisy environment," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    4. Gajda, Janusz & Bartnicki, Grzegorz & Burnecki, Krzysztof, 2018. "Modeling of water usage by means of ARFIMA–GARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 644-657.
    5. Adriano Zanin Zambom & Seonjin Kim & Nancy Lopes Garcia, 2022. "Variable length Markov chain with exogenous covariates," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 312-328, March.
    6. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    7. Burnecki, Krzysztof & Sikora, Grzegorz, 2017. "Identification and validation of stable ARFIMA processes with application to UMTS data," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 456-466.

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