An Entropy-Based Approach to Measurement of Stock Market Depth

The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.     

Dynamics of a Diffusion Malaria Model With Vector-Bias北大核心CSCD

为了探讨季节性、蚊子叮咬的偏好性和人类的扩散对疟疾传播的影响,该文提出了一个部分退化的周期反应扩散模型.利用动力系统的持续性理论,研究了模型关于基本再生数R₀的阈值动力学.即当R₀<1时,疾病灭绝;而当R₀>1时,疾病一致持续,且会发生季节性的流行.数值上发现了忽略空间异质性和蚊子叮咬的偏好性会低估疾病传染的风险.     

A short survey on delay differential systems with periodic coefficients

In this survey, we collect a few results scatted in the literature covering advances in systems of periodic delay differential equations including both modeling and theory. We will present the (almost) most oldest and (almost) most recent contributions made for this subject.     

Optimal bed net use for a dengue disease model with mosquito seasonal pattern

Controversial results concerning the effectiveness of bed net in reducing dengue fever transmission make further research necessary in this direction. At this aim, we consider a mathematical model of dengue transmission where the use by individuals of insecticide‐treated bed nets is taken into account, combined or not with insecticide spraying. Furthermore, as climatic factors play a key role in mosquito‐borne diseases, we model the effect of seasonality through a periodic mosquito birth rate. We numerically investigate some specific scenarios according to different rainfall and mean temperature values. We set an optimal control problem to minimize the number of human infections and the cost of efforts placed into bed net adoption and maintenance and insecticide spraying. To assess the most appropriate strategy to eliminate dengue with minimum costs, we perform a comparative cost‐effectiveness analysis, which also shows how the cost‐benefit of intervention efforts is affected by changes in the amplitude of seasonal variation. One general result is that in any case the combination of bed net use and insecticide spraying produces the highest ratio of infections averted, whereas in terms of cost‐benefit only spraying campaigns should be implemented in control programs for regions with no large seasonality.     

Asymptotic Properties of Estimators for Seasonally Cointegrated State Space Models Obtained Using the CVA Subspace Method

This paper investigates the asymptotic properties of estimators obtained from the so called CVA (canonical variate analysis) subspace algorithm proposed by Larimore (1983) in the case when the data is generated using a minimal state space system containing unit roots at the seasonal frequencies such that the yearly difference is a stationary vector autoregressive moving average (VARMA) process. The empirically most important special cases of such data generating processes are the I(1) case as well as the case of seasonally integrated quarterly or monthly data. However, increasingly also datasets with a higher sampling rate such as hourly, daily or weekly observations are available, for example for electricity consumption. In these cases the vector error correction representation (VECM) of the vector autoregressive (VAR) model is not very helpful as it demands the parameterization of one matrix per seasonal unit root. Even for weekly series this amounts to 52 matrices using yearly periodicity, for hourly data this is prohibitive. For such processes estimation using quasi-maximum likelihood maximization is extremely hard since the Gaussian likelihood typically has many local maxima while the parameter space often is high-dimensional. Additionally estimating a large number of models to test hypotheses on the cointegrating rank at the various unit roots becomes practically impossible for weekly data, for example. This paper shows that in this setting CVA provides consistent estimators of the transfer function generating the data, making it a valuable initial estimator for subsequent quasi-likelihood maximization. Furthermore, the paper proposes new tests for the cointegrating rank at the seasonal frequencies, which are easy to compute and numerically robust, making the method suitable for automatic modeling. A simulation study demonstrates by example that for processes of moderate to large dimension the new tests may outperform traditional tests based on long VAR approximations in sample sizes typically found in quarterly macroeconomic data. Further simulations show that the unit root tests are robust with respect to different distributions for the innovations as well as with respect to GARCH-type conditional heteroskedasticity. Moreover, an application to Kaggle data on hourly electricity consumption by different American providers demonstrates the usefulness of the method for applications. Therefore the CVA algorithm provides a very useful initial guess for subsequent quasi maximum likelihood estimation and also delivers relevant information on the cointegrating ranks at the different unit root frequencies. It is thus a useful tool for example in (but not limited to) automatic modeling applications where a large number of time series involving a substantial number of variables need to be modelled in parallel.     

Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives

Daily average temperature variations are modelled with a mean‐reverting Ornstein–Uhlenbeck process driven by a generalized hyperbolic Lévy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean‐reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME).     

Study of the Seasonal Variations of the Fatty Acid Profiles of Selected Macroalgae

Due to the high consumption of fat-rich processed foods, efforts are being done to reduce their saturated fat (SFA) contents and replace it with polyunsaturated fatty acids (PUFA), creating a necessity to find alternative PUFA sources. Macroalgae, being a promising natural source of healthy food, may be such an alternative. The fatty acid (FA) profile of Fucus spiralis, Bifurcaria bifurcata, Ulva lactuca, and Saccorhiza polyschides were determined through direct transesterification and their seasonal variation was studied. F. spiralis showed the highest FA content overall, B. bifurcata presented the higher PUFA amounts, and U. lactuca and S. polyschides the higher SFA. The production of FA was shown to be influenced by the seasons. Spring and summer seemed to induce the FA production in F. spiralis and B. bifurcata while in U. lactuca the same was verified in winter. U. lactuca presented a ω6/ω3 ratio between 0.59 and 1.38 while B. bifurcata presented a ratio around 1.31. The study on the seasonal variations of the macroalgal FA profile can be helpful to understand the best season to yield FA of interest, such as ALA, EPA, and DHA. It may also provide valuable information on the best culturing conditions for the production of desired FAs.     

NMR‐based approach reveals seasonal metabolic changes in mate (Ilex paraguariensis A. St.‐Hil.)

Ilex paraguariensis (mate) is a species native to South America and is widely consumed in countries such Argentina, Uruguay, Paraguay, and Brazil. Mate consumption is associated with several phytotherapeutic functions, in addition to its cultural and regional importance. However, the harvest period can affect the properties of the mate, due to variations in the constituent proportions, as a consequence of seasonal changes. In this work, we employed nuclear magnetic resonance and chemometrics to evaluate the chemical variations in leaf extracts of I. paraguariensis over the four seasons of the year. We found significant changes in the levels of glucose, myo‐inositol, caffeine, theobromine, and fatty acids. These changes can be related to resource allocation for the flowering period, or to responses to environmental stresses, such as temperature.     

Harvesting canthinones: identification of the optimal seasonal point of harvest of Zanthoxylum chiloperone leaves as a source of 5-methoxycanthin-6-one

This article is focused on the seasonal variation in the contents of 5-methoxycanthin-6-one from the leaves of Zanthoxylum chiloperone (Rutaceae). Based on the pharmacological interest presented by 5-methoxycanthin-6-one, its seasonal variation in Z. chiloperone leaves was analysed in order to determine the best time for harvesting, optimising the 5-methoxycanthin-6-one content. The seasonal dynamics of canthinone alkaloids can be the key to improve the isolation from natural sustainable sources, such as leaves. Complementarily, this study describes the phytochemistry of leaf from this Ruraceae species.