INSTRUMENTAL VARIABLE ESTIMATION OF STRUCTURAL VAR MODELS ROBUST TO POSSIBLE NONSTATIONARITY

This paper considers the estimation of dynamic causal effects using a proxy structural vector-autoregressive model with possibly nonstationary regressors. We provide general conditions under which the asymptotic normal approximation remains valid. In this case, the asymptotic variance depends on the persistence property of each series. We further provide a consistent asymptotic covariance matrix estimator that requires neither knowledge of the presistence properties of the variables nor pretests for nonstationarity. The proposed consistent covariance matrix estimator is robust and is easy to implement in practice. When all regressors are indeed stationary, the method becomes the same as the standard procedure.

Comparative analysis of the stock quotes dynamics for IT-sector and the entertainment industry companies based on the characteristics of memory depth

The article is devoted to the study and comparative analysis of the stock quotes dynamics for the world’s leading companies in the IT sector and the entertainment industry. Today, these areas are developing the fastest and most powerful, which attracts the attention of investors around the world. This is due to the rapid development of digital communication technologies, the growth of intellectualization and individualization of goods and services, and so on. These spheres have strong development potential, but the question to how their companies’ stock quotes respond to the impact of such a natural but crisis phenomenon as the COVID-19 pandemic remains open. Based on the nonlinear paradigm of the financial markets dynamics, the paper considers and conducts a comprehensive fractal analysis of the quotations dynamics for six leading companies (Apple Inc., Tesla Inc., Alphabet Inc., The Walt Disney Company, Sony Corporation, Netflix) in this area before and during the COVID-19 pandemic. As a result of the application of the rescaled range analysis (R/S analysis), the presence of the persistence property and long-term memory in the stock quotes dynamics for all companies and its absence in their time series of profitability was confirmed. The application of the method of sequential R/S analysis made it possible to construct fuzzy sets of memory depths for the considered time series and to deepen the analysis of the dynamics due to the quantitative characteristics calculated on their basis. Taking into account the characteristics of memory depth in the dynamics of quotations made it possible to conduct a comparative analysis of the dynamics, both under the influence of the natural crisis situation and in terms of investing in different terms. The peculiarities of the delayed profitability dynamics of quotations for each of the companies are also taken into consideration and compared. The developed recommendations can be used in investment activities in the stock market.

Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting

A reaction–diffusion interacting species system with Beddington–DeAngelis functional response that has been proposed in the environment of mathematical ecology, which provides the rise to spatial pattern formation, is investigated and associated with the models of deterministic dynamics. The dynamical behaviour of a generalist predator–prey system with linear harvesting of each species and predator-dependent functional response is fully analyzed. Conditions of stability behaviour of the interior equilibrium point are established properly. Furthermore, we have recognized that the unique positive equilibrium point of the system is globally stable via appropriate Lyapunov function structure, which signifies that appropriate harvesting has no impact on the persistence property of the harvesting system. Also, we establish the conditions for the existence of bifurcation phenomena including a saddle-node bifurcation and a Hopf bifurcation. Subsequently, complete analysis regarding the impact of harvesting is carried out, and an interesting decision is that under some appropriate constraints, harvesting has immense impact on the final size of the interacting species. In addition, in accordance with Turing’s ideas on morphogenesis , our analysis shows that harvesting effort in a reaction–diffusion predator–prey system plays a vital function for geological conservation of interacting species. Finally, we discuss sufficient conditions for the existence of bionomic equilibrium point and the optimal harvesting policy attained by using the Pontryagin maximal principle.

Well-posedness and behaviors of solutions to an integrable evolution equation

This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and uniqueness of analytic solutions with analytic initial values are established. The solutions are analytic for both variables, globally in space and locally in time. The effects of coefficients λ and β on the solutions are given.

Sortable Simplicial Complexes and $t$-Independence Ideals of Proper Interval Graphs

We introduce the notion of sortability and $t$-sortability for a simplicial complex and study the graphs for which their independence complexes are either sortable or $t$-sortable. We show that the proper interval graphs are precisely the graphs whose independence complex is sortable. By using this characterization, we show that the ideal generated by all squarefree monomials corresponding to independent sets of vertices of $G$ of size $t$ (for a given positive integer $t$) has the strong persistence property, when $G$ is a proper interval graph. Moreover, all of its powers have linear quotients.

A family of monomial ideals with the persistence property

In this paper, we introduce a family of monomial ideals with the persistence property. Given positive integers [Formula: see text] and [Formula: see text], we consider the monomial ideal [Formula: see text] generated by all monomials [Formula: see text], where [Formula: see text] is an independent set of vertices of the path graph [Formula: see text] of size [Formula: see text], which is indeed the facet ideal of the [Formula: see text]th skeleton of the independence complex of [Formula: see text]. We describe the set of associated primes of all powers of [Formula: see text] explicitly. It turns out that any such ideal [Formula: see text] has the persistence property. Moreover, the index of stability of [Formula: see text] and the stable set of associated prime ideals of [Formula: see text] are determined.

Diagnostics of a persistence property for quotations dynamics on high-tech stock markets

The research purpose is diagnosis of the persistence property for the stock quotes time series of leading companies belonging to the high-tech sector: Apple Inc., Microsoft Corporation and Samsung Electronics Co. The persistence property or the trend-stability of the time series is crucial meaning for the investor. As a result of the application of the R\S-analysis, it is proved that the stock quotations dynamics of these companies have the persistence property. Also, the method of sequential R\S analysis is applied: the leading characteristics of the long-term memory are discovered, which makes it possible to carry out a comparative analysis of their predictability. It is found that the time series of profitability do not have the properties of persistence. However, the tests for diagnostic of a deterministic chaos reveal the appearance of the persistence property in the time series of “delayed” profitability. The obtained results allows to state the fractal nature for the time series of quotations, while the characteristics of the persistence (depth of memory) determined by the research can be useful to the investor in terms of the investment instrument choice and the investment horizon as well as can be used in selecting the parameters for a forecasting model.