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Evaluations of likelihood based surveillance of volatility

Author

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  • Bock, David

    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

The volatility of asset returns are important in finance. Different likelihood based methods of statistical surveillance for detecting a change in the variance are evaluated. The differences are how the partial likelihood ratios are weighted. The full likelihood ratio, Shiryaev-Roberts, Shewhart and the CUSUM methods are derived in case of an independent and identically distributed Gaussian process. The behavior of the methods is studied both when there is no change and when the change occurs at different time points. The false alarms are controlled by the median run length. Differences and limiting equalities of the methods are shown. The performances when the process parameters for which the methods are optimized for differ from the true values of the parameters are evaluated. The methods are illustrated on a period of Standard and Poor’s 500 stock market index.

Suggested Citation

  • Bock, David, 2007. "Evaluations of likelihood based surveillance of volatility," Research Reports 2007:9, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    • Handle: RePEc:hhs:gunsru:2007_009
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    File URL: http://hdl.handle.net/2077/8477
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    References listed on IDEAS

    as
    1. Frisén, Marianne, 2007. "Principles for Multivariate Surveillance," Research Reports 2007:4, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    2. Marianne Frisén, 2003. "Statistical Surveillance. Optimality and Methods," International Statistical Review, International Statistical Institute, vol. 71(2), pages 403-434, August.
    3. Elena Andreou & Eric Ghysels, 2002. "Detecting multiple breaks in financial market volatility dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 579-600.
    4. Bock, David, 2007. "Consequences of using the probability of a false alarm as the false alarm measure," Research Reports 2007:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    5. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    6. Andersson, Eva, 2007. "Effect of dependency in systems for multivariate surveillance," Research Reports 2007:1, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    7. Frisén, Marianne, 2007. "Optimal Sequential Surveillance for Finance, Public Health, and Other Areas," Research Reports 2007:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    8. E. Andersson & D. Bock & M. Frisen, 2006. "Some statistical aspects of methods for detection of turning points in business cycles," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 257-278.
    9. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Similarities and differences between statistical surveillance and certain decision rules in finance," Research Reports 2007:8, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    10. Christian Sonesson & David Bock, 2003. "A review and discussion of prospective statistical surveillance in public health," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 5-21, February.
    11. Andersson, Eva & Bock, David & Frisén, Marianne, 2007. "Modeling influenza incidence for the purpose of on-line monitoring," Research Reports 2007:5, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    12. Bock, David & Andersson, Eva & Frisén, Marianne, 2007. "Statistical Surveillance of Epidemics: Peak Detection of Influenza in Sweden," Research Reports 2007:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    13. A. F. B. Costa & M. A. Rahim, 2004. "Monitoring Process Mean and Variability with One Non-central Chi-square Chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(10), pages 1171-1183.
    14. Eva Andersson & David Bock & Marianne Frisén, 2004. "Detection of Turning Points in Business Cycles," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2004(1), pages 93-108.
    15. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Schiöler, Linus, 2009. "Explorative analysis of spatial patterns of influenza incidences in Sweden 1999—2008," Research Reports 2008:5, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    2. Schiöler, Linus & Frisén, Marianne, 2008. "On statistical surveillance of the performance of fund managers," Research Reports 2008:4, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    3. Andersson, Eva, 2008. "Hotelling´s T2 Method in Multivariate On-line Surveillance. On the Delay of an Alarm," Research Reports 2008:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    4. Frisén, Marianne, 2011. "Methods and evaluations for surveillance in industry, business, finance, and public health," Research Reports 2011:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    5. Frisén, Marianne & Andersson, Eva & Schiöler, Linus, 2009. "Sufficient reduction in multivariate surveillance," Research Reports 2009:2, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

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    More about this item

    Keywords

    surveillance; statistical process control; monitoring; likelihood ratio; Shewhart; CUSUM;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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