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|
|Publication status:||Published in Econometric Reviews (2008), 27(1-3): 254-267|
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- 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.
- Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
- 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.
- 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.
- K Abadir & W Distaso & L Giraitis, "undated". "Local Whittle estimation, fully extended for nonstationarity," Discussion Papers 05/16, Department of Economics, University of York.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002.
"Modeling and Forecasting Realized Volatility,"
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.
- 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.
- 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.
- 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.
- Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
- Rohit Deo & Clifford Hurvich & Yi Lu, 2005.
"Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment,"
- 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.
- 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.
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