Asymmetry of Information Flow between Volatilities Across 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.

Gold, oil, and stocks: Dynamic correlations

“…2 trading classes at different investment horizons (Gençay et al, 2010). Third, heterogeneity of market behavior coupled with interactions among assets might result in dynamic correlations among assets that would exhibit less-than-obvious patterns.…”

Linear and nonlinear causality between renewable energy consumption and economic growth in the USA

“…It is relatively recent that wavelet analysis was used for specific aim in economics and finance. The recent literature relating to its application can be seen in Gençay et al (2010), Bogdanova (2015), Benhmad (2013), Rasti (2016), Alzahrani, Masih, Wu (2014) and Al-Titi (2014) among the others.…”

Portfolio Value at Risk Estimate for Crude Oil Markets: A Multivariate Wavelet Denoising Approach

“…However, it is found that the originally proposed test statistics is upward biased heavily if models tested are nested. Thus the Clark-West test of equal predictive accuracy is proposed to incorporate this important nested model structure in forecast evaluation problems and adjust for the DM statistics as in (23).…”

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