Asymmetry of Information Flow between Volatilities Across Time Scales

40 Pages Posted: 5 May 2003 Last revised: 17 Jun 2009

See all articles by Ramazan Gencay

Ramazan Gencay

Simon Fraser University

Faruk Selcuk

Bilkent University - Department of Economics

Nikola Gradojevic

University of Guelph, Department of Economics and Finance; University of Bologna - Rimini Center for Economic Analysis (RCEA)

Brandon Whitcher

National Center for Atmospheric Research

Date Written: June 2009

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.

Keywords: Discrete wavelet transform, wavelet-domain hidden Markov trees, foreign exchange markets, stock markets, multiresolution analysis, scaling, Finance, Financial Econometrics, Volatility, High-Frequency Finance, Wavelets

JEL Classification: G0, G1, C1

Suggested Citation

Gencay, Ramazan and Selcuk, Faruk and Gradojevic, Nikola and Whitcher, Brandon, Asymmetry of Information Flow between Volatilities Across Time Scales (June 2009). Available at SSRN: https://ssrn.com/abstract=386400 or http://dx.doi.org/10.2139/ssrn.386400

Ramazan Gencay (Contact Author)

Simon Fraser University ( email )

Department of Economics
8888 University Drive
Burnaby, British Columbia V5A 1S6
Canada

Faruk Selcuk

Bilkent University - Department of Economics ( email )

06800 Ankara
Turkey
+90 (312) 290 2074 (Phone)
+90 (312) 266-5140 (Fax)

HOME PAGE: www.bilkent.edu.tr/~faruk

Nikola Gradojevic

University of Guelph, Department of Economics and Finance ( email )

50 Stone Road East
Guelph, Ontario N1G 2W1
Canada

HOME PAGE: http://https://www.uoguelph.ca/economics/users/nikola-gradojevic

University of Bologna - Rimini Center for Economic Analysis (RCEA) ( email )

Via Patara, 3
Rimini (RN), RN 47900
Italy

Brandon Whitcher

National Center for Atmospheric Research ( email )

P.O. Box 3000
Boulder, CO 80307
United States

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