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Functional data analysis for volatility

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  • Müller, Hans-Georg
  • Sen, Rituparna
  • Stadtmüller, Ulrich

Abstract

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets and describe functional representations and data-based recovery of the process from repeated observations. A study of its asymptotic properties, as the frequency of observed trades increases, is complemented by simulations and an application to the analysis of intra-day volatility patterns of the S&P 500 index. The proposed volatility model is found to be useful to identify recurring patterns of volatility and for successful prediction of future volatility, through the application of functional regression and prediction techniques.

Suggested Citation

  • Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    • Handle: RePEc:eee:econom:v:165:y:2011:i:2:p:233-245
    DOI: 10.1016/j.jeconom.2011.08.002
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    1. Tong, Howell & Yao, Qiwei, 2000. "Nonparametric estimation of ratios of noise to signal in stochastic regression," LSE Research Online Documents on Economics 6324, London School of Economics and Political Science, LSE Library.
    2. Muller, Hans-Georg & Stadtmuller, Ulrich & Yao, Fang, 2006. "Functional Variance Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1007-1018, September.
    3. Fang Yao & Hans-Georg Müller & Andrew J. Clifford & Steven R. Dueker & Jennifer Follett & Yumei Lin & Bruce A. Buchholz & John S. Vogel, 2003. "Shrinkage Estimation for Functional Principal Component Scores with Application to the Population Kinetics of Plasma Folate," Biometrics, The International Biometric Society, vol. 59(3), pages 676-685, September.
    4. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    5. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    6. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    7. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
    8. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
    9. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    10. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    11. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    12. 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.
    13. 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.
    14. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    15. Alan E.H. Speight & David G. McMillan & Owain ap Gwilym, 2000. "Intra‐day volatility components in FTSE‐100 stock index futures," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 20(5), pages 425-444, May.
    16. S. Sanfelici & S. Ogawa, 2008. "An improved two-step regularization scheme for spot volatility estimation," Economics Department Working Papers 2008-ME02, Department of Economics, Parma University (Italy).
    17. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-174, January.
    18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    19. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    20. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    21. Mancino, M.E. & Sanfelici, S., 2008. "Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2966-2989, February.
    22. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(1), pages 60-93, February.
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    1. Miguel Martínez Comesaña & Sandra Martínez Mariño & Pablo Eguía Oller & Enrique Granada Álvarez & Aitor Erkoreka González, 2020. "A Functional Data Analysis for Assessing the Impact of a Retrofitting in the Energy Performance of a Building," Mathematics, MDPI, vol. 8(4), pages 1-20, April.
    2. Shang, Han Lin & Kearney, Fearghal, 2022. "Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1025-1049.
    3. Maeng, Hye Young & Fryzlewicz, Piotr, 2019. "Regularised forecasting via smooth-rough partitioning of the regression coefficients," LSE Research Online Documents on Economics 100878, London School of Economics and Political Science, LSE Library.
    4. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    5. Jan G. De Gooijer & Cees G. H. Diks & Łukasz T. Gątarek, 2012. "Information Flows Around the Globe: Predicting Opening Gaps from Overnight Foreign Stock Price Patterns," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(1), pages 23-44, March.
    6. Horváth, Lajos & Rice, Gregory, 2015. "Testing for independence between functional time series," Journal of Econometrics, Elsevier, vol. 189(2), pages 371-382.
    7. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    8. Han Lin Shang & Yang Yang & Fearghal Kearney, 2019. "Intraday forecasts of a volatility index: functional time series methods with dynamic updating," Annals of Operations Research, Springer, vol. 282(1), pages 331-354, November.
    9. Kearney, Fearghal & Murphy, Finbarr & Cummins, Mark, 2015. "An analysis of implied volatility jump dynamics: Novel functional data representation in crude oil markets," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 199-216.
    10. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    11. Bo Li & Sabri Boubaker & Zhenya Liu & Waël Louhichi & Yao Yao, 2023. "Exploring the Nonlinear Idiosyncratic Volatility Puzzle: Evidence from China," Computational Economics, Springer;Society for Computational Economics, vol. 62(2), pages 527-559, August.
    12. Wang, Deqing & Tian, Sihua & Fang, Lei & Xu, Yan, 2020. "A functional index model for dynamically evaluating China's energy security," Energy Policy, Elsevier, vol. 147(C).
    13. Zhenjie Liang & Futian Weng & Yuanting Ma & Yan Xu & Miao Zhu & Cai Yang, 2022. "Measurement and Analysis of High Frequency Assert Volatility Based on Functional Data Analysis," Mathematics, MDPI, vol. 10(7), pages 1-11, April.
    14. Yu, Chao & Fang, Yue & Zhao, Xujie & Zhang, Bo, 2013. "Kernel filtering of spot volatility in presence of Lévy jumps and market microstructure noise," MPRA Paper 63293, University Library of Munich, Germany, revised 10 Mar 2014.
    15. B. Cooper Boniece & Lajos Horv'ath & Lorenzo Trapani, 2023. "On changepoint detection in functional data using empirical energy distance," Papers 2310.04853, arXiv.org.
    16. Horváth, Lajos & Kokoszka, Piotr & Rice, Gregory, 2014. "Testing stationarity of functional time series," Journal of Econometrics, Elsevier, vol. 179(1), pages 66-82.
    17. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2019. "Tests for conditional heteroscedasticity with functional data and goodness-of-fit tests for FGARCH models," MPRA Paper 93048, University Library of Munich, Germany.
    18. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    19. Ofélia Anjos & Miguel Martínez Comesaña & Ilda Caldeira & Soraia Inês Pedro & Pablo Eguía Oller & Sara Canas, 2020. "Application of Functional Data Analysis and FTIR-ATR Spectroscopy to Discriminate Wine Spirits Ageing Technologies," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    20. Ma, Haiqiang & Zhu, Zhongyi, 2016. "Continuously dynamic additive models for functional data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 1-13.
    21. Thibault Vatter & Hau-Tieng Wu & Valérie Chavez-Demoulin & Bin Yu, 2015. "Non-Parametric Estimation of Intraday Spot Volatility: Disentangling Instantaneous Trend and Seasonality," Econometrics, MDPI, vol. 3(4), pages 1-24, December.
    22. Shang, Han Lin, 2017. "Functional time series forecasting with dynamic updating: An application to intraday particulate matter concentration," Econometrics and Statistics, Elsevier, vol. 1(C), pages 184-200.
    23. Tomáš Rubín & Victor M. Panaretos, 2020. "Functional lagged regression with sparse noisy observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 858-882, November.

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    More about this item

    Keywords

    Diffusion model; Functional principal component; Functional regression; High frequency trading; Market returns; Prediction; Volatility process; Trajectories of volatility;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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