Information flow between volatilities across time scales
AbstractConventional 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 10355.
Date of creation: Oct 2004
Date of revision:
Discrete wavelet transform; wavelet-domain hidden Markov trees; foreign exchange markets; stock markets; multiresolution analysis; scaling;
Find related papers by JEL classification:
- C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
- G00 - Financial Economics - - General - - - General
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
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