IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v256y2017i1p163-177.html
   My bibliography  Save this article

Relevant states and memory in Markov chain bootstrapping and simulation

Author

Listed:
  • Cerqueti, Roy
  • Falbo, Paolo
  • Pelizzari, Cristian

Abstract

Markov chain theory is proving to be a powerful approach to bootstrap and simulate highly nonlinear time series. In this work, we provide a method to estimate the memory of a Markov chain (i.e. its order) and to identify its relevant states. In particular, the choice of memory lags and the aggregation of irrelevant states are obtained by looking for regularities in the transition probabilities. Our approach is based on an optimization model. More specifically, we consider two competing objectives that a researcher will in general pursue when dealing with bootstrapping and simulation: preserving the “structural” similarity between the original and the resampled series, and assuring a controlled diversification of the latter. A discussion based on information theory is developed to define the desirable properties for such optimal criteria. Two numerical tests are developed to verify the effectiveness of the proposed method.

Suggested Citation

  • Cerqueti, Roy & Falbo, Paolo & Pelizzari, Cristian, 2017. "Relevant states and memory in Markov chain bootstrapping and simulation," European Journal of Operational Research, Elsevier, vol. 256(1), pages 163-177.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:163-177
    DOI: 10.1016/j.ejor.2016.06.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171630426X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2016.06.006?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stanislav Anatolyev & Andrey Vasnev, 2002. "Markov chain approximation in bootstrapping autoregressions," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-8.
    2. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data‐Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, vol. 54(5), pages 1647-1691, October.
    3. M. Rajarshi, 1990. "Bootstrap in Markov-sequences based on estimates of transition density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 253-268, June.
    4. Chao, Gary H., 2013. "Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders," European Journal of Operational Research, Elsevier, vol. 225(3), pages 383-392.
    5. Buhlmann, Peter & Kunsch, Hans R., 1999. "Block length selection in the bootstrap for time series," Computational Statistics & Data Analysis, Elsevier, vol. 31(3), pages 295-310, September.
    6. White, Chelsea C. & White, Douglas J., 1989. "Markov decision processes," European Journal of Operational Research, Elsevier, vol. 39(1), pages 1-16, March.
    7. White, D. J., 1987. "Infinite horizon Markov decision processes with unknown or variable discount factors," European Journal of Operational Research, Elsevier, vol. 28(1), pages 96-100, January.
    8. Ohno, Katsuhisa & Boh, Toshitaka & Nakade, Koichi & Tamura, Takayoshi, 2016. "New approximate dynamic programming algorithms for large-scale undiscounted Markov decision processes and their application to optimize a production and distribution system," European Journal of Operational Research, Elsevier, vol. 249(1), pages 22-31.
    9. Cerqueti, Roy & Falbo, Paolo & Guastaroba, Gianfranco & Pelizzari, Cristian, 2013. "A Tabu Search heuristic procedure in Markov chain bootstrapping," European Journal of Operational Research, Elsevier, vol. 227(2), pages 367-384.
    10. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    11. Paparoditis, Efstathios & Politis, Dimitris N., 2001. "A Markovian Local Resampling Scheme For Nonparametric Estimators In Time Series Analysis," Econometric Theory, Cambridge University Press, vol. 17(3), pages 540-566, June.
    12. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    13. Efstathios Paparoditis & Dimitris N. Politis, 2002. "The tapered block bootstrap for general statistics from stationary sequences," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 131-148, June.
    14. repec:ebl:ecbull:v:3:y:2002:i:19:p:1-8 is not listed on IDEAS
    15. José M. Bernardo & Raúl Rueda, 2002. "Bayesian Hypothesis Testing: a Reference Approach," International Statistical Review, International Statistical Institute, vol. 70(3), pages 351-372, December.
    16. Buhlmann P., 2002. "Sieve Bootstrap With Variable-Length Markov Chains for Stationary Categorical Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 443-471, June.
    17. Pandelis, Dimitrios G., 2010. "Markov decision processes with multidimensional action spaces," European Journal of Operational Research, Elsevier, vol. 200(2), pages 625-628, January.
    18. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
    19. Hall, Peter, 1985. "Resampling a coverage pattern," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 231-246, September.
    20. Patrice Bertail & Stéphan Clémençon, 2007. "Second-order properties of regeneration-based bootstrap for atomic Markov chains," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 109-122, May.
    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. Roy Cerqueti & Paolo Falbo & Cristian Pelizzari & Federica Ricca & Andrea Scozzari, 2017. "A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping," Annals of Operations Research, Springer, vol. 248(1), pages 163-187, January.
    2. Arias, Mariz B. & Kim, Myungchin & Bae, Sungwoo, 2017. "Prediction of electric vehicle charging-power demand in realistic urban traffic networks," Applied Energy, Elsevier, vol. 195(C), pages 738-753.
    3. Chen, Yi-Ting & Sun, Edward W. & Lin, Yi-Bing, 2020. "Merging anomalous data usage in wireless mobile telecommunications: Business analytics with a strategy-focused data-driven approach for sustainability," European Journal of Operational Research, Elsevier, vol. 281(3), pages 687-705.

    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. Bertail, Patrice & Clemencon, Stephan, 2008. "Approximate regenerative-block bootstrap for Markov chains," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2739-2756, January.
    2. Roy Cerqueti & Paolo Falbo & Cristian Pelizzari & Federica Ricca & Andrea Scozzari, 2017. "A mixed integer linear program to compress transition probability matrices in Markov chain bootstrapping," Annals of Operations Research, Springer, vol. 248(1), pages 163-187, January.
    3. Manzan, S. & Zerom, D., 2005. "A Multi-Step Forecast Density," CeNDEF Working Papers 05-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. Manzan, Sebastiano & Zerom, Dawit, 2008. "A bootstrap-based non-parametric forecast density," International Journal of Forecasting, Elsevier, vol. 24(3), pages 535-550.
    5. Nomikos, Nikos K. & Doctor, Kaizad, 2013. "Economic significance of market timing rules in the Forward Freight Agreement markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 52(C), pages 77-93.
    6. Jessica James & Louis Yang, 2010. "Stop-losses, maximum drawdown-at-risk and replicating financial time series with the stationary bootstrap," Quantitative Finance, Taylor & Francis Journals, vol. 10(1), pages 1-12.
    7. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2011. "Cross-sectional dependence robust block bootstrap panel unit root tests," Journal of Econometrics, Elsevier, vol. 163(1), pages 85-104, July.
    8. Stephan Schulmeister, 2000. "Technical Analysis and Exchange Rate Dynamics," WIFO Studies, WIFO, number 25857.
    9. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    10. Edwin D. Maberly & Daniel F. Waggoner, 2000. "Closing the question on the continuation of turn-of-the-month effects: evidence from the S&P 500 Index futures contract," FRB Atlanta Working Paper 2000-11, Federal Reserve Bank of Atlanta.
    11. Ma-Ju Wang, 2014. "A Study on the Differences in Adopting Cash Refund Capital Reduction and Stock Repurchase By Companies in Bull and Bear Stock Markets," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 4(9), pages 1237-1253, September.
    12. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    13. Zakamulin, Valeriy & Giner, Javier, 2022. "Time series momentum in the US stock market: Empirical evidence and theoretical analysis," International Review of Financial Analysis, Elsevier, vol. 82(C).
    14. 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.
    15. Jin, Xiaoye, 2022. "Testing technical trading strategies on China's equity ETFs: A skewness perspective," Emerging Markets Review, Elsevier, vol. 51(PA).
    16. Shynkevich, Andrei, 2013. "Time-series momentum as an intra- and inter-industry effect: Implications for market efficiency," Journal of Economics and Business, Elsevier, vol. 69(C), pages 64-85.
    17. Guo, Bin & Huang, Fuzhe & Li, Kai, 2022. "Time to build and bond risk premia," Journal of Economic Dynamics and Control, Elsevier, vol. 136(C).
    18. Martin Scholtus & Dick van Dijk, 2012. "High-Frequency Technical Trading: The Importance of Speed," Tinbergen Institute Discussion Papers 12-018/4, Tinbergen Institute.
    19. Michael D. McKenzie, 2007. "Technical Trading Rules in Emerging Markets and the 1997 Asian Currency Crises," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 43(4), pages 46-73, August.
    20. Guanqing Liu, 2019. "Technical Trading Behaviour: Evidence from Chinese Rebar Futures Market," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 669-704, August.

    More about this item

    Keywords

    Bootstrapping; Information theory; Markov chains; Optimization; Simulation;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

    Statistics

    Access and download statistics

    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:ejores:v:256:y:2017:i:1:p:163-177. 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.elsevier.com/locate/eor .

    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.