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A study on modeling the dynamics of statistically dependent returns

Author

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  • Davari-Ardakani, Hamed
  • Aminnayeri, Majid
  • Seifi, Abbas

Abstract

This paper develops a method to characterize the dynamic behavior of statistically dependent returns of assets via a scenario set. The proposed method uses heteroskedastic time series to model serial correlations of returns, as well as Cholesky decomposition to generate the set of scenarios such that the statistical dependence of different asset returns is preserved. In addition, this scenario generation method preserves marginal distributions of returns. To demonstrate the performance of the proposed method, a multi-period portfolio optimization model is presented. Then, the method is implemented through a number of stocks selected from New York Stock Exchange (NYSE). Computational results show a high performance of the proposed method from the statistical point of view. Also, results confirm sufficiency and in-sample stability of the generated scenario set. Besides, out-of-sample simulations, for both risk and return, illustrate a good performance of the proposed method.

Suggested Citation

  • Davari-Ardakani, Hamed & Aminnayeri, Majid & Seifi, Abbas, 2014. "A study on modeling the dynamics of statistically dependent returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 35-51.
    • Handle: RePEc:eee:phsmap:v:405:y:2014:i:c:p:35-51
    DOI: 10.1016/j.physa.2014.02.077
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Densing, M., 2012. "Occupation times of the Ornstein–Uhlenbeck process: Functional PCA and evidence from electricity prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 5818-5826.
    3. Zhiping Chen & K. C. Yuen, 2005. "Optimal consumption and investment problems under GARCH with transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(2), pages 219-237, June.
    4. Christina Erlwein & Gautam Mitra & Diana Roman, 2012. "HMM based scenario generation for an investment optimisation problem," Annals of Operations Research, Springer, vol. 193(1), pages 173-192, March.
    5. Pieter Klaassen, 2002. "Comment on "Generating Scenario Trees for Multistage Decision Problems"," Management Science, INFORMS, vol. 48(11), pages 1512-1516, November.
    6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    7. Fleten, Stein-Erik & Hoyland, Kjetil & Wallace, Stein W., 2002. "The performance of stochastic dynamic and fixed mix portfolio models," European Journal of Operational Research, Elsevier, vol. 140(1), pages 37-49, July.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Bernaschi, Massimo & Tacconi, Elisa & Vergni, Davide, 2008. "A parametric study of the term structure dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1264-1272.
    10. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    11. Gulpinar, Nalan & Rustem, Berc & Settergren, Reuben, 2004. "Simulation and optimization approaches to scenario tree generation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1291-1315, April.
    12. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
    13. 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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