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Minimum chi-squared estimation of stable distributions parameters: An application to the Warsaw Stock Exchange

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  • Zbigniew Kominek
Abstract
This paper derives an application of the minimum chi-squared (MCS) methodology to estimate the parameters of the unimodal symmetric stable distribution. The proposed method is especially suitable for large, both regular and non-standard, data sets. Monte Carlo simulations are performed to compare the efficiency of the MCS estimation with the efficiency of the McCulloch quantile algorithm. In the case of grouped observations, evidence in favour of the MCS method is reported. For the ungrouped data the MCS estimation generally performs better than McCulloch's quantile method for samples larger than 400 observations and for high alphas. The relative advantage of the MCS over the McCulloch estimators increases for larger samples. The empirical example analyses the highly irregular distributions of returns on the selected securities from the Warsaw Stock Exchange. The quantile and maximum likelihood estimates of characteristic exponents are generally smaller than the MCS ones. This reflects the bias in the traditional methods, which is due to a lack of adjustment for censored and clustered observations, and shows the flexibility of the proposed MCS approach.

Suggested Citation

  • Zbigniew Kominek, 2002. "Minimum chi-squared estimation of stable distributions parameters: An application to the Warsaw Stock Exchange," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 729-744.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:729-744
    DOI: 10.1080/02664760120098793
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    References listed on IDEAS

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    1. Charemza, Wojciech W. & Majerowska, Ewa, 2000. "Regulation of the Warsaw Stock Exchange: The portfolio allocation problem," Journal of Banking & Finance, Elsevier, vol. 24(4), pages 555-576, April.
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    3. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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