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Asymmetry of information flow between volatilities across time scales


Gençay, Ramazan; Gradojevic, Nikola; Selçuk, Faruk; Whitcher, Brandon (2012). Asymmetry of information flow between volatilities across time scales. Quantitative Finance, 10(8):895-915.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Scopus Subject Areas:Social Sciences & Humanities > Finance
Social Sciences & Humanities > General Economics, Econometrics and Finance
Language:English
Date:2012
Deposited On:24 Nov 2020 10:02
Last Modified:25 Nov 2020 21:00
Publisher:Taylor & Francis
ISSN:1469-7688
OA Status:Closed
Publisher DOI:https://doi.org/10.1080/14697680903460143
Official URL:https://www.tandfonline.com/doi/full/10.1080/14697680903460143
Other Identification Number:merlin-id:5968

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