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

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Author Info
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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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

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  6. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-53, December. [Downloadable!] (restricted)
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  7. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
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  8. Ole Barndorff-Nielsen & Neil Shephard, 2000. "Non-Gaussian OU based models and some of their uses in financial economics," OFRC Working Papers Series 2000mf01, Oxford Financial Research Centre. [Downloadable!]
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  10. John Y. Campbell & Martin Lettau, 1999. "Dispersion and Volatility in Stock Returns: An Empirical Investigation," NBER Working Papers 7144, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. 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. [Downloadable!] (restricted)
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  15. 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.
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  17. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 12(5), pages 937-74.
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