Maximum Rényi Entropy Rate Bunte, Christoph; Lapidoth, Amos
IEEE transactions on information theory,
2016-March, 2016-3-00, 20160301, Letnik:
62, Številka:
3
Journal Article
Recenzirano
The supremum of the Rényi entropy rate over the class of discrete-time stationary stochastic processes, whose marginals are supported by some given set and satisfy some given cost constraint, is ...computed. Unlike the Shannon entropy, the Rényi entropy of a random vector can exceed the sum of the Rényi entropies of its components, and the supremum is, therefore, typically not achieved by memoryless processes. It is nonetheless related to Shannon's entropy: when the Rényi parameter exceeds one, the supremum is equal to the corresponding supremum of Shannon's entropy, and when it is smaller than one, the supremum equals the logarithm of the volume of the support set. A Burg-like supremum of the Rényi entropy rate over the class of stochastic processes, whose autocovariance function begins with some given values, is also solved. It is not achieved by Gauss-Markov processes, but it is nonetheless related to Burg's supremum: the two are equal when the Rényi parameter exceeds one, and the former is infinite otherwise.
Since time-frequency (TF) analysis can provide TF information for characterizing the time-varying signals, TF analysis is a powerful tool for analyzing the nonstationary (N-S) signals. An important ...task of TF analysis is to yield a sharp TF representation that energy distribution is highly concentrated at an instantaneous frequency (IF) in the TF plane. In order to yield concentrated TF representation on the premise of signal reconstruction, this article proposes a local maximum synchrosqueezing transform (LMSST)-based TF analysis method with time-varying window and time-varying searching region. In particular, the adaptive window with the time-varying function is employed to suppress the violation produced by time-varying frequency characteristics. Here, the time-varying function is optimized based on the local Rényi entropy. Also, the local maximum of the TF coefficients is computed within the time-varying region to be the estimator of the IF of the signals. The time-varying region is employed to match different kinds of signals. In the meantime, it is proved that the signals can be reconstructed. The computer numerical simulation results show that our work yields sharper TF representation than the existing methods. Also, reconstructed signals are closer to the origin signals. In addition, the effectiveness of the proposed method is validated on real-world signals that contain the stationary signals and the N-S signals.
•Via Renyi entropy we analyze the multiscale entropy measurement of global markets.•By estimating mutual information we expose the dependencies and information flow.•Randomness and disorder are more ...observed in low probability events.•The information sharing network among markets was modified during COVID-19 pandemic.•We offer a valuable insight of the impact of COVID-19 pandemic upon expectations and investor fear.
The COVID-19 pandemic has seriously affected world economies. In this regard, it is expected that information level and sharing between equity, digital currency, and energy markets has been altered due to the pandemic outbreak. Specifically, the resulting twisted risk among markets is presumed to rise during the abnormal state of world economy. The purpose of the current study is twofold. First, by using Renyi entropy, we analyze the multiscale entropy function in the return time series of Bitcoin, S&P500, WTI, Brent, Gas, Gold, Silver, and investor fear index represented by VIX. Second, by estimating mutual information, we analyze the information sharing between these markets. The analyses are conducted before and during the COVID-19 pandemic. The empirical results from Renyi entropy indicate that for all market indices, randomness and disorder are more concentrated in less probable events. The empirical results from mutual information showed that the information sharing network between markets has changed during the COVID-19 pandemic. From a managerial perspective, we conclude that during the pandemic (i) portfolios composed of Bitcoin and Silver, Bitcoin and WTI, Bitcoin and Gold, Bitcoin and Brent, or Bitcoin and S&P500 could be risky, (ii) diversification opportunities exist by investing in portfolios composed of Gas and Silver, Gold and Silver, Gold and Gas, Brent and Silver, Brent and Gold, or Bitcoin and Gas, and that (iii) the VIX exhibited the lowest level of information disorder at all scales before and during the pandemic. Thus, it seems that the pandemic has not influenced the expectations of investors. Our results provide an insight of the response of stocks, cryptocurrencies, energy, precious metal markets, to expectations of investors in the aftermath of the COVID-19 pandemic in terms of information ordering and sharing.
The principle of maximum entropy is employed to derive the shear stress distribution by maximizing the Renyi entropy subject to some constraints and by assuming that dimensionless shear stress is a ...random variable. A Renyi entropy-based equation can be used to model the shear stress distribution along the entire wetted perimeter of circular channels and circular channels with flat beds and deposited sediments. A wide range of experimental results for 12 hydraulic conditions with different Froude numbers (0.375 to 1.71) and flow depths (20.3 to 201.5 mm) were used to validate the derived shear stress distribution. For circular channels, model performance enhanced with increasing flow depth (mean relative error (RE) of 0.0414) and only deteriorated slightly at the greatest flow depth (RE of 0.0573). For circular channels with flat beds, the Renyi entropy model predicted the shear stress distribution well at lower sediment depth. The Renyi entropy model results were also compared with Shannon entropy model results. Both models performed well for circular channels, but for circular channels with flat beds the Renyi entropy model displayed superior performance in estimating the shear stress distribution. The Renyi entropy model was highly precise and predicted the shear stress distribution in a circular channel with RE of 0.0480 and in a circular channel with a flat bed with RE of 0.0488.
•Renyi entropy concept is maximized with the help of Lagrange coefficients.•An equation for predicting shear stress along the perimeter in circular channels is derived.•The accuracy of the proposed model is verified with validated experimental results.
It is well-known that returns of financial assets exhibit heavy tail property and there has been no distribution which can reliably capture this characteristic so far. To contribute to the solution ...of this problem, we derive a new heavy tail distribution using the maximum entropy principle for Renyi entropy under the absolute moment constraints. Our newly derived distribution with two shape parameters forms a family of distributions. They are smooth, scaleable, symmetric and may be heavy tailed if their shape parameter attains the appropriate value. As a result, parameters of this distribution can be estimated by maximum likelihood estimation technique. The ability of the derived distribution to model the heavy tail property of financial assets is verified on a range of financial instruments. The results we obtained show that it can be a better option for modeling the returns of financial assets compared to other well-known heavy tailed distributions.
•The maximum Renyi entropy principle is used to derive a heavy-tailed distribution•It has two shape parameters similar to the generalized t-distribution•Its PDF and CDF are without non-linear constraints on its parameters•It is a better model for modeling the returns of traditional financial assets
This paper proposes a new type of entropy called Renyi entropy as an extension of logarithm entropy in an uncertain random environment and applies it to portfolio selection. We first define Renyi ...entropy and partial Renyi entropy to measure the indeterminacy of uncertain random variables and examine their mathematical properties. Then, we provide an approach for calculating partial Renyi entropy for uncertain random variables through Monte Carlo simulation. Next, we introduce Renyi cross-entropy and the concept of partial Renyi cross-entropy of uncertain random variables. As an application in finance, partial Renyi entropy is invoked to optimize portfolio selection of uncertain random returns. Numerical examples are displayed for illustration purposes. Finally, we compare the investment strategies adopted by the mean-Renyi entropy models with those of the mean-elliptic entropy models and the mean-variance models.
The power forecasting plays a significant role in the electrical systems. Furthermore the high-dimensional data reduction without losing essential information represents an important advantage in the ...forecasting models. Low computational costs and short execution time together with high predicted performance are the main goals to be reached in the development of a prediction method. In this paper a hybrid method based on an active selection of the support vectors, using the quadratic Renyi entropy criteria in combination with the principal component analysis (PCA), is shown to dimensionally reduce the training data in the forecasting models. The reduced data have been used to implement the Least Squares Support Vector Machines (LS-SVM) in order to predict the photovoltaic (PV) power in the day-ahead time horizon. The model has been validated using historical data of a PV system in the Mediterranean climate. Additionally the weather variations have been taken into account to evaluate the outcome of the sunny and cloudy condition in the PV forecasting models. The proposed technique gives fulfill results. A training data size same as 30% original dimension allows to improve the forecasting accuracy and reduces the computational time of 70% respect to an implementation without dimensionality reduction data.
•A dimensionally reduction technique, based on the Renyi entropy and PCA is shown.•LS-SVM models are applied to predict the PV output power in a one-day head frame.•Photovoltaic forecasting model is performed using the historical PV power data.•The predicted method considers the weather conditions as sunny and cloudy days.•The accuracy and executive time of the hybrid method has been investigated.
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