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Asymmetry of Information Flow Between Volatilities Across Time Scales

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  • Ramazan Gencay
  • Faruk Selcuk

Abstract

Conventional time series analysis, focusing exclusively on a time series at a given scale, lacks the ability to explain the nature of the data generating process. A process equation that successfully explains daily price changes, for example, is unable to characterize the nature of hourly price changes. On the other hand, statistical properties of monthly price changes are often not fully covered by a model based on daily price changes. In this paper, we simultaneously model regimes of volatilities at multiple time scales through wavelet-domain hidden Markov models. We establish an important stylized property of volatility across different time scales. We call this property asymmetric vertical dependence. It is asymmetric in the sense that a low volatility state (regime) at a long time horizon is most likely followed by low volatility states at shorter time horizons. On the other hand, a high volatility state at long time horizons does not necessarily imply a high volatility state at shorter time horizons. Our analysis provides evidence that volatility is a mixture of high and low volatility regimes, resulting in a distribution that is non-Gaussian. This result has important implications regarding the scaling behavior of volatility, and consequently, the calculation of risk at different time scales.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 90.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nawm04:90

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Keywords: Volatility; High Frequency Finance; Wavelets; Hidden Markov Trees;

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Cited by:
  1. Benhmad, Fran├žois, 2012. "Modeling nonlinear Granger causality between the oil price and U.S. dollar: A wavelet based approach," Economic Modelling, Elsevier, vol. 29(4), pages 1505-1514.
  2. Kaijian He & Kin Keung Lai & Guocheng Xiang, 2012. "Portfolio Value at Risk Estimate for Crude Oil Markets: A Multivariate Wavelet Denoising Approach," Energies, MDPI, Open Access Journal, vol. 5(4), pages 1018-1043, April.
  3. Jozef Barunik & Lukas Vacha, 2012. "Realized wavelet-based estimation of integrated variance and jumps in the presence of noise," Papers 1202.1854, arXiv.org, revised Feb 2013.
  4. Fran├žois Benhmad, 2011. "A wavelet analysis of oil price volatility dynamic," Economics Bulletin, AccessEcon, vol. 31(1), pages 792-806.
  5. Jozef Barunik & Lukas Vacha, 2012. "Modeling and forecasting exchange rate volatility in time-frequency domain," Papers 1204.1452, arXiv.org, revised Aug 2013.
  6. Gallegati, Marco & Ramsey, James B., 2013. "Bond vs stock market's Q: Testing for stability across frequencies and over time," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 138-150.

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