Measuring Dispersion and Serial Dependence in Ordinal Time Series Based on the Cumulative Paired ϕ-Entropy

The family of cumulative paired ϕ-entropies offers a wide variety of ordinal dispersion measures, covering many well-known dispersion measures as a special case. After a comprehensive analysis of this family of entropies, we consider the corresponding sample versions and derive their asymptotic distributions for stationary ordinal time series data. Based on an investigation of their asymptotic bias, we propose a family of signed serial dependence measures, which can be understood as weighted types of Cohen’s κ, with the weights being related to the actual choice of ϕ. Again, the asymptotic distribution of the corresponding sample κϕ is derived and applied to test for serial dependence in ordinal time series. Using numerical computations and simulations, the practical relevance of the dispersion and dependence measures is investigated. We conclude with an environmental data example, where the novel ϕ-entropy-related measures are applied to an ordinal time series on the daily level of air quality.

Asymptotic behavior of dependence measures for Ornstein-Uhlenbeck model based on long memory processes

In this paper, we study the long memory property of two processes based on the Ornstein-Uhlenbeck model. Their are extensions of the Ornstein-Uhlenbeck system for which in the classic version we replace the standard Brownian motion (or other L$$\acute{e}$$ e ´ vy process) by long range dependent processes based on $$\alpha -$$ α - stable distribution. One way of characterizing long- and short-range dependence of second order processes is in terms of autocovariance function. However, for systems with infinite variance the classic measure is not defined, therefore there is a need to consider alternative measures on the basis of which the long range dependence can be recognized. In this paper, we study three alternative measures adequate for $$\alpha -$$ α - stable-based processes. We calculate them for examined processes and indicate their asymptotic behavior. We show that one of the analyzed Ornstein-Uhlenbeck process exhibits long memory property while the second does not. Moreover, we show the ratio of two introduced measures is limited which can be a starting point to introduction of a new estimation method of stability index for analyzed Ornstein-Uhlenbeck processes.

Analysis of the dependence structure for time series of hedge funds returns

The aim of the thesis is to emphasize the different dependence measures beyond the well known Pearson correlation. The study is developed in the setting of a fund that deals with multiple strategies hedge funds under risk constraints. The relevance of our analysis is made clears by noticing that the Pearson correlation is sensitive only to linear relationships and it does not capture tail co-movements. Specifically, the dependence measures we focus are Kendall's tau, Spearman's rho and tail dependence. This thesis attempts to suggest some other solutions to an effective optimization that combines various fund strategies by using the aforementioned dependence measures.

Analysis of the dependence structure for time series of hedge funds returns

The aim of the thesis is to emphasize the different dependence measures beyond the well known Pearson correlation. The study is developed in the setting of a fund that deals with multiple strategies hedge funds under risk constraints. The relevance of our analysis is made clears by noticing that the Pearson correlation is sensitive only to linear relationships and it does not capture tail co-movements. Specifically, the dependence measures we focus are Kendall's tau, Spearman's rho and tail dependence. This thesis attempts to suggest some other solutions to an effective optimization that combines various fund strategies by using the aforementioned dependence measures.

Validating E-cigarette Dependence Scales Based on Dynamic Patterns of Vaping Behaviors

Introduction Existing e-cigarette dependence scales are mainly validated based on retrospective overall consumption or perception. Further, given that the majority of adult e-cigarette users also use combustible cigarettes, it is important to determine whether e-cigarette dependence scales capture the product-specific dependence. This study fills in the current knowledge gaps by validating e-cigarette dependence scales using novel indices of dynamic patterns of e-cigarette use behaviors and examining the association between dynamic patterns of smoking and e-cigarette dependence among dual users. Methods Secondary analysis was conducted on the 2-week ecological momentary assessment data from 116 dual users. The Smoothly Clipped Absolute Deviation penalty (SCAD) was adopted to select important indices for dynamic patterns of consumption or craving and estimate their associations with e-cigarette dependence scales. Results The fitted linear regression models support the hypothesis that higher e-cigarette dependence is associated with higher levels of e-cigarette consumption and craving as well as lower instability of e-cigarette consumption. Controlling for dynamic patterns of vaping, dual users with lower e-cigarette dependence tend to report higher day-to-day dramatic changes in combustible cigarette consumption but not higher average levels of smoking. Conclusions We found that more stable use patterns are related to higher levels of dependence, which has been demonstrated in combustible cigarettes and we have now illustrated in e-cigarettes. Furthermore, the e-cigarette dependence scales may capture the product-specific average consumption but not product-specific instability of consumption. Implications This study provides empirical support for three e-cigarette dependence measures: PS-ECDI, e-FTCD, and e-WISDM, based on dynamic patterns of e-cigarette consumption and craving revealed by EMA data that have great ecological validity. This is the first study that introduces novel indices of dynamic patterns and demonstrates their potential applications in vaping research.