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Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results

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  • Elena Andreou
  • Eric Ghysels

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Abstract

We propose different extensions of the continuous record asymptotic analysis for rolling sample variance estimators developed by Foster and Nelson (1996). First, despite the difference in information sets we are able to compare the asymptotic distribution of volatility estimators involving data sampled at different frequencies. We focus on traditional historical volatility filters involving monthly, daily and intra-daily observations. Second, we introduce a continuous record asymptotics approach for estimating the so called integrated volatility, which represents the cumulative integral of instantaneous volatility. The new approach treats integrated volatility as a stochastic process sampled at high frequencies and suggests rolling sample estimators which share many features with spot volatility estimators. We discuss optimal weighting schemes for integrated volatility estimators. Thirdly, we establish the links between various spot and integrated volatility estimators. Theoretical results are complemented with extensive Monte Carlo simulations and an empirical investigation. Nous proposons des extensions de la théorie asymptotique de Foster et Nelson pour l'estimation de variance. Nous proposons une approximation asymptotique qui permet de comparer des estimateurs obtenus à partir de données avec fréquences d'échantillonnage différentes. Une autre extension consiste à appliquer les arguments de Foster et Nelson à des processus plus généraux tels que la volatilité intégrée.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2000s-19.

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Date of creation: 01 May 2000
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Handle: RePEc:cir:cirwor:2000s-19

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Keywords: High-frequency data; volatility; continuous record asymptotics; Monte Carlo simulations; Données haute fréquence; volatilité; Monte Carlo;

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  1. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-74.
  2. Campbell, John Y & Kim, Sangjoon & Lettau, Martin, 1998. "Dispersion and Volatility in Stock Returns: An Empirical Investigation," CEPR Discussion Papers 1923, C.E.P.R. Discussion Papers.
  3. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
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  7. Bollerslev, Tim & Domowitz, Ian, 1993. " Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-43, September.
  8. James M. Poterba & Lawrence H. Summers, 1984. "The Persistence of Volatility and Stock Market Fluctuations," NBER Working Papers 1462, National Bureau of Economic Research, Inc.
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
  10. Malkiel, Burton & Campbell, John & Lettau, Martin & Xu, Yexiao, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Scholarly Articles 3128707, Harvard University Department of Economics.
  11. Foster, Dean P & Nelson, Daniel B, 1996. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," Econometrica, Econometric Society, vol. 64(1), pages 139-74, January.
  12. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  13. G. William Schwert, 1990. "Stock Volatility and the Crash of '87," NBER Working Papers 2954, National Bureau of Economic Research, Inc.
  14. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May.
  15. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
  16. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  17. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  18. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  19. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  20. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
  21. 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.
  22. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-77, December.
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