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Volatility estimation and jump detection for drift–diffusion processes

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  • Laurent, Sébastien
  • Shi, Shuping
Abstract
The logarithmic prices of financial assets are conventionally assumed to follow a drift–diffusion process. While the drift term is typically ignored in the infill asymptotic theory and applications, the presence of temporary nonzero drifts is an undeniable fact. The finite sample theory for integrated variance estimators and extensive simulations provided in this paper reveal that the drift component has a nonnegligible impact on the estimation accuracy of volatility, which leads to a dramatic power loss for a class of jump identification procedures. We propose an alternative construction of volatility estimators and observe significant improvement in the estimation accuracy in the presence of nonnegligible drift. The analytical formulas of the finite sample bias of the realized variance, bipower variation, and their modified versions take simple and intuitive forms. The new jump tests, which are constructed from the modified volatility estimators, show satisfactory performance. As an illustration, we apply the new volatility estimators and jump tests, along with their original versions, to 21 years of 5-minute log returns of the NASDAQ stock price index.

Suggested Citation

  • Laurent, Sébastien & Shi, Shuping, 2020. "Volatility estimation and jump detection for drift–diffusion processes," Journal of Econometrics, Elsevier, vol. 217(2), pages 259-290.
    • Handle: RePEc:eee:econom:v:217:y:2020:i:2:p:259-290
    DOI: 10.1016/j.jeconom.2019.12.004
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    1. Ana-Maria Dumitru & Giovanni Urga, 2011. "Identifying Jumps in Financial Assets: A Comparison Between Nonparametric Jump Tests," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 242-255, October.
    2. Campbell, John Y & Hamao, Yasushi, 1992. "Predictable Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration," Journal of Finance, American Finance Association, vol. 47(1), pages 43-69, March.
    3. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    4. Rychlik, Tomasz, 1994. "Distributions and expectations of order statistics for possibly dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 31-42, January.
    5. Campbell, John Y & Ammer, John, 1993. "What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns," Journal of Finance, American Finance Association, vol. 48(1), pages 3-37, March.
    6. Kim Christensen & Roel Oomen & Roberto Renò, 2016. "The Drift Burst Hypothesis," CREATES Research Papers 2016-28, Department of Economics and Business Economics, Aarhus University.
    7. Lo, Andrew W & Wang, Jiang, 1995. "Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March.
    8. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    9. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    10. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    11. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    12. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    13. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    14. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    15. Chaudhuri, Kausik & Wu, Yangru, 2003. "Random walk versus breaking trend in stock prices: Evidence from emerging markets," Journal of Banking & Finance, Elsevier, vol. 27(4), pages 575-592, April.
    16. Shuping Shi & Yong Song, 2016. "Identifying Speculative Bubbles Using an Infinite Hidden Markov Model," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 159-184.
    17. Lee, Suzanne S. & Mykland, Per A., 2012. "Jumps in equilibrium prices and market microstructure noise," Journal of Econometrics, Elsevier, vol. 168(2), pages 396-406.
    18. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    19. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466, October.
    20. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    21. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    22. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    23. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    24. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    25. Bekaert, Geert & Hodrick, Robert J, 1992. "Characterizing Predictable Components in Excess Returns on Equity and Foreign Exchange Markets," Journal of Finance, American Finance Association, vol. 47(2), pages 467-509, June.
    26. Ronald Balvers & Yangru Wu & Erik Gilliland, 2000. "Mean Reversion across National Stock Markets and Parametric Contrarian Investment Strategies," Journal of Finance, American Finance Association, vol. 55(2), pages 745-772, April.
    27. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 1-37.
    28. Peter C. B. Phillips & Shuping Shi, 2019. "Detecting Financial Collapse and Ballooning Sovereign Risk," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(6), pages 1336-1361, December.
    29. Dominicy, Yves & Hörmann, Siegfried & Ogata, Hiroaki & Veredas, David, 2013. "On sample marginal quantiles for stationary processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 28-36.
    30. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    31. Zhou, Qiankun & Yu, Jun, 2015. "Asymptotic theory for linear diffusions under alternative sampling schemes," Economics Letters, Elsevier, vol. 128(C), pages 1-5.
    32. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    33. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    34. Bessembinder, Hendrik & Chan, Kalok, 1992. "Time-varying risk premia and forecastable returns in futures markets," Journal of Financial Economics, Elsevier, vol. 32(2), pages 169-193, October.
    35. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
    36. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    37. repec:taf:jnlbes:v:30:y:2012:i:2:p:242-255 is not listed on IDEAS
    38. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
    39. Lee, Suzanne S. & Hannig, Jan, 2010. "Detecting jumps from Lévy jump diffusion processes," Journal of Financial Economics, Elsevier, vol. 96(2), pages 271-290, May.
    40. Boudt, Kris & Laurent, Sébastien & Lunde, Asger & Quaedvlieg, Rogier & Sauri, Orimar, 2017. "Positive semidefinite integrated covariance estimation, factorizations and asynchronicity," Journal of Econometrics, Elsevier, vol. 196(2), pages 347-367.
    41. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    42. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December.
    43. Andersen, Torben G. & Bollerslev, Tim & Dobrev, Dobrislav, 2007. "No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and i.i.d. noise: Theory and testable distributional implications," Journal of Econometrics, Elsevier, vol. 138(1), pages 125-180, May.
    44. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
    45. repec:bla:jfinan:v:53:y:1998:i:1:p:219-265 is not listed on IDEAS
    46. Etienne, Xiaoli L. & Irwin, Scott H. & Garcia, Philip, 2014. "Bubbles in food commodity markets: Four decades of evidence," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 129-155.
    47. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    48. Boudt, Kris & Croux, Christophe & Laurent, Sébastien, 2011. "Robust estimation of intraweek periodicity in volatility and jump detection," Journal of Empirical Finance, Elsevier, vol. 18(2), pages 353-367, March.
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    2. Cui, Tianxiang & Suleman, Muhammad Tahir & Zhang, Hongwei, 2022. "Do the green bonds overreact to the COVID-19 pandemic?," Finance Research Letters, Elsevier, vol. 49(C).
    3. Chae-Deug, Yi, 2024. "Realized normal volatility and maximum outlying jumps in high frequency returns for Korean won–US Dollar," International Review of Financial Analysis, Elsevier, vol. 95(PA).
    4. Qiu, Yue & Wang, Zongrun & Xie, Tian & Zhang, Xinyu, 2021. "Forecasting Bitcoin realized volatility by exploiting measurement error under model uncertainty," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 179-201.
    5. Shuping Shi & Peter C. B. Phillips, 2022. "Econometric Analysis of Asset Price Bubbles," Cowles Foundation Discussion Papers 2331, Cowles Foundation for Research in Economics, Yale University.
    6. YI, Chae-Deug, 2023. "Exchange rate volatility and intraday jump probability with periodicity filters using a local robust variance," Finance Research Letters, Elsevier, vol. 55(PA).
    7. Ahmed, Walid M.A., 2021. "How do Islamic equity markets respond to good and bad volatility of cryptocurrencies? The case of Bitcoin," Pacific-Basin Finance Journal, Elsevier, vol. 70(C).
    8. Nabil Bouamara & S'ebastien Laurent & Shuping Shi, 2023. "Sequential Cauchy Combination Test for Multiple Testing Problems with Financial Applications," Papers 2303.13406, arXiv.org, revised Jun 2023.

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    More about this item

    Keywords

    Diffusion process; Nonzero drift; Finite sample theory; Volatility estimation; Jumps;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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