IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v83y2012icp56-79.html
   My bibliography  Save this article

Further properties of random orthogonal matrix simulation

Author

Listed:
  • Ledermann, Daniel
  • Alexander, Carol

Abstract

Random orthogonal matrix (ROM) simulation is a very fast procedure for generating multivariate random samples that always have exactly the same mean, covariance and Mardia multivariate skewness and kurtosis. This paper investigates how the properties of parametric, data-specific and deterministic ROM simulations are influenced by the choice of orthogonal matrix. Specifically, we consider how cyclic and general permutation matrices alter their time-series properties, and how three classes of rotation matrices – upper Hessenberg, Cayley, and exponential – influence both the unconditional moments of the marginal distributions and the behaviour of skewness when samples are concatenated. We also perform an experiment which demonstrates that parametric ROM simulation can be hundreds of times faster than equivalent Monte Carlo simulation.

Suggested Citation

  • Ledermann, Daniel & Alexander, Carol, 2012. "Further properties of random orthogonal matrix simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 56-79.
    • Handle: RePEc:eee:matcom:v:83:y:2012:i:c:p:56-79
    DOI: 10.1016/j.matcom.2012.07.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475412001784
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2012.07.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    2. McAleer, Michael & da Veiga, Bernardo & Hoti, Suhejla, 2011. "Value-at-Risk for country risk ratings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1454-1463.
    3. Yang, Yung-Lieh & Chang, Chia-Lin, 2008. "A double-threshold GARCH model of stock market and currency shocks on stock returns," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 458-474.
    4. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    5. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    6. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    7. Allen, David E. & McAleer, Michael & Scharth, Marcel, 2011. "Monte Carlo option pricing with asymmetric realized volatility dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1247-1256.
    8. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    9. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    10. Hörmann, Wolfgang & Sak, Halis, 2010. "t-Copula generation for control variates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 782-790.
    11. Yip, Iris W.H. & So, Mike K.P., 2009. "Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 327-340.
    12. Chen, Cathy W.S. & Gerlach, Richard H. & Tai, Amanda P.J., 2008. "Testing for nonlinearity in mean and volatility for heteroskedastic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 489-499.
    13. Burq, Zaeem A. & Jones, Owen D., 2008. "Simulation of Brownian motion at first-passage times," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 64-71.
    14. Bi, Guang & Giles, David E., 2009. "Modelling the financial risk associated with U.S. movie box office earnings," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2759-2766.
    15. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    16. Sevastianov, P. & Dymova, L., 2009. "Synthesis of fuzzy logic and Dempster–Shafer Theory for the simulation of the decision-making process in stock trading systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 506-521.
    17. Allen, David E. & Gao, Jiti & McAleer, Michael, 2009. "Modelling and managing financial risk: An overview," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2521-2524.
    18. Pulch, Roland & van Emmerich, Cathrin, 2009. "Polynomial chaos for simulating random volatilities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 245-255.
    19. Doan, Viet_Dung & Gaikwad, Abhijeet & Bossy, Mireille & Baude, Françoise & Stokes-Rees, Ian, 2010. "Parallel pricing algorithms for multi-dimensional Bermudan/American options using Monte Carlo methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 568-577.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexander, Carol & Meng, Xiaochun & Wei, Wei, 2022. "Targeting Kollo skewness with random orthogonal matrix simulation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 362-376.
    2. Geyer, Alois & Hanke, Michael & Weissensteiner, Alex, 2014. "No-Arbitrage ROM simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 66-79.
    3. Hanke, Michael & Penev, Spiridon & Schief, Wolfgang & Weissensteiner, Alex, 2017. "Random orthogonal matrix simulation with exact means, covariances, and multivariate skewness," European Journal of Operational Research, Elsevier, vol. 263(2), pages 510-523.
    4. Carol Alexander & Xiaochun Meng & Wei Wei, 2020. "Targetting Kollo Skewness with Random Orthogonal Matrix Simulation," Papers 2004.06586, arXiv.org, revised Sep 2021.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Psaradellis, Ioannis & Laws, Jason & Pantelous, Athanasios A. & Sermpinis, Georgios, 2023. "Technical analysis, spread trading, and data snooping control," International Journal of Forecasting, Elsevier, vol. 39(1), pages 178-191.
    2. Dan Anghel, 2013. "How Reliable is the Moving Average Crossover Rule for an Investor on the Romanian Stock Market?," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 5(2), pages 089-115, December.
    3. Alvaro Escribano & Genaro Sucarrat, 2011. "Automated model selection in finance: General-to-speci c modelling of the mean and volatility speci cations," Working Papers 2011-09, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    4. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
    5. Costantini, Mauro & Cuaresma, Jesus Crespo & Hlouskova, Jaroslava, 2014. "Can Macroeconomists Get Rich Forecasting Exchange Rates?," Economics Series 305, Institute for Advanced Studies.
    6. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, vol. 24(2), pages 404-447, April.
    7. Dichtl, Hubert & Drobetz, Wolfgang & Neuhierl, Andreas & Wendt, Viktoria-Sophie, 2021. "Data snooping in equity premium prediction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 72-94.
    8. Isakov, Dusan & Marti, Didier, 2011. "Technical Analysis with a Long-Term Perspective: Trading Strategies and Market Timing Ability," FSES Working Papers 421, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    9. Jin, Sainan & Corradi, Valentina & Swanson, Norman R., 2017. "Robust Forecast Comparison," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1306-1351, December.
    10. Hsu, Po-Hsuan & Hsu, Yu-Chin & Kuan, Chung-Ming, 2010. "Testing the predictive ability of technical analysis using a new stepwise test without data snooping bias," Journal of Empirical Finance, Elsevier, vol. 17(3), pages 471-484, June.
    11. Christophe Hurlin & Sébastien Laurent & Rogier Quaedvlieg & Stephan Smeekes, 2017. "Risk Measure Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 499-512, October.
    12. Raffaella Giacomini & Barbara Rossi, 2013. "Forecasting in macroeconomics," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 17, pages 381-408, Edward Elgar Publishing.
    13. Byunghoon Kang, 2018. "Inference in Nonparametric Series Estimation with Specification Searches for the Number of Series Terms," Working Papers 240829404, Lancaster University Management School, Economics Department.
    14. Hasanov, Akram Shavkatovich & Shaiban, Mohammed Sharaf & Al-Freedi, Ajab, 2020. "Forecasting volatility in the petroleum futures markets: A re-examination and extension," Energy Economics, Elsevier, vol. 86(C).
    15. Shynkevich, Andrei, 2012. "Short-term predictability of equity returns along two style dimensions," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 675-685.
    16. Nakashima, Kiyotaka & Saito, Makoto, 2012. "On the comparison of alternative specifications for money demand: The case of extremely low interest rate regimes in Japan," Journal of the Japanese and International Economies, Elsevier, vol. 26(3), pages 454-471.
    17. David E. Rapach & Jack K. Strauss, 2008. "Structural breaks and GARCH models of exchange rate volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 65-90.
    18. Håvard Hungnes, 2020. "Equal predictability test for multi-step-ahead system forecasts invariant to linear transformations," Discussion Papers 931, Statistics Norway, Research Department.
    19. Yang, Junmin & Cao, Zhiguang & Han, Qiheng & Wang, Qiyu, 2019. "Tactical asset allocation on technical trading rules and data snooping," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    20. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:83:y:2012:i:c:p:56-79. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.