Refined Inference on Long Memory in Realized Volatility
There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et al. (2004)). The present paper provides some analytical explanations for this evidence and shows how recent results in Lieberman and Phillips (2004a, 2004b) can be used to refine statistical inference about d with little computational effort. In contrast to standard asymptotic normal theory now used in the literature which has an O(n-1/2) error rate on error rejection probabilities, the asymptotic approximation used here has an error rate of o(n-1/2). The new formula is independent of unknown parameters, is simple to calculate and highly user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et. al. (2001) and Martens et. al. (2004) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory.
|Date of creation:||Jan 2006|
|Date of revision:|
|Publication status:||Published in Econometric Reviews (2008), 27(1-3): 254-267|
|Contact details of provider:|| Postal: |
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC
|Order Information:|| Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011.
"Edgeworth expansions for realized volatility and related estimators,"
Journal of Econometrics,
Elsevier, vol. 160(1), pages 190-203, January.
- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2005. "Edgeworth Expansions for Realized Volatility and Related Estimators," NBER Technical Working Papers 0319, National Bureau of Economic Research, Inc.
- Andersen, Torben G & Bollerslev, Tim, 1997.
" Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns,"
Journal of Finance,
American Finance Association, vol. 52(3), pages 975-1005, July.
- Torben G. Andersen & Tim Bollerslev, 1996. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," NBER Working Papers 5752, National Bureau of Economic Research, Inc.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001.
"Modeling and Forecasting Realized Volatility,"
Center for Financial Institutions Working Papers
01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- Federico Bandi & Benoit Perron, 2003.
"Long memory and the relation between implied and realized volatility,"
- Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 636-670.
- Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006.
"Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment,"
Journal of Econometrics,
Elsevier, vol. 131(1-2), pages 29-58.
- Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA.
- Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
- Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
- Offer Lieberman & Peter C.B. Phillips, 2004.
"Expansions for Approximate Maximum Likelihood Estimators of the Fractional Difference Parameter,"
Cowles Foundation Discussion Papers
1474, Cowles Foundation for Research in Economics, Yale University.
- Offer Lieberman & Peter C. B. Phillips, 2005. "Expansions for approximate maximum likelihood estimators of the fractional difference parameter," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 367-379, December.
- 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.
- Yacine Aït-Sahalia, 2005.
"How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise,"
Review of Financial Studies,
Society for Financial Studies, vol. 18(2), pages 351-416.
- Yacine Ait-Sahalia & Per A. Mykland, 2003. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," NBER Working Papers 9611, National Bureau of Economic Research, Inc.
- K Abadir & W Distaso & L Giraitis, . "Local Whittle estimation, fully extended for nonstationarity," Discussion Papers 05/16, Department of Economics, University of York.
- Neil Shephard, 2005.
Economics Series Working Papers
2005-W17, University of Oxford, Department of Economics.
- 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.
- Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
- 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.
- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003.
"A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data,"
NBER Working Papers
10111, National Bureau of Economic Research, Inc.
- 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.
- Lieberman, Offer & Phillips, Peter C.B., 2004. "Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter," Econometric Theory, Cambridge University Press, vol. 20(03), pages 464-484, June.
When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1549. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Glena Ames)
If references are entirely missing, you can add them using this form.