Analysis of the high order ADL(p, q) models used to describe connections between time series

In the paper the mathematical models describing connection between two time series are researched. At first each of them is investigated separately, and the ARIMA(p, d, q) model is constructed. These models are based on the time series characteristics obtained during the analysis stage. The connection between two time series is confirmed with the aid of cointegration statistical tests. Then the mathematical model of the connection between series is constructed. The ADL(p, q) model describes this dependence. It’s shown that for the time series under investigation the orders p, q of the ADL(p, q) model are connected with the ARIMA(p, d, q) orders of the describing each series separately. This step makes the set of the investigated ADL(p, q) models much smaller. In the previous papers it was also shown that the ARIMA(p, d, q) automatical fitting functions in popular packages use limitations on the p, q orders of the time series process: q ≤ 5, p ≤ 5. The wish to use the simplest models is also built in the structure of the Akaike (AIC) and Bayes (BIC) informational criteria. In the paper the maximal values of the ADL(p, q) model orders are supposed to be the orders of the appropriate ARIMA(p, d, q) series. In the previous work it was shown that using high order ARIMA(p, d, q) it is possible to fit the models better. In this paper the experiments on the ADL(p, q) models construction are presented. The wage index and money income index time series pair is researched, and also the gas, water and energy production and consumption index/real agricultural production index pair is investigated. The data in the 2000–2018 time period is taken from the dynamic series of macroeconomic statistics of the Russian Federation.

On Computer-Assisted Proving The Existence Of Periodic And Bounded Orbits

We announce a new result on determining the Conley index of the Poincaré map for a time-periodic non-autonomous ordinary differential equation. The index is computed using some singular cycles related to an index pair of a small-step discretization of the equation. We indicate how the result can be applied to computer-assisted proofs of the existence of bounded and periodic solutions. We provide also some comments on computer-assisted proving in dynamics.

Analysis of Pd-Ni Nanobelts Melting Process Using Molecular Dynamics Simulation

The melting process of Pd-Ni alloy nanobelts with different Ni atom content has been simulated by molecular dynamic (MD) method. The radial distribution function, the Lindemann index, and pair analysis method were used to characterize Pd-Ni nanobelt models in simulation. The results indicate that the melting temperature of Pd-Ni nanobelt with composition far from pure metal was lower than that of other models, and the breaking point of the nanobelt can be illustrated by the Lindemann index. Pair analysis indicates that the number of FCC pairs will decrease and almost disappear at melting point with increasing temperature. The melting points of Pd-Ni alloy nanobelts were also calculated by thermodynamic method, and the results were close to that obtained by MD simulation.

SPATIAL CONFIGURATION OF ATOMS WITH HIGH-ENERGY ATOMIC DISPLACEMENT CASCADE IN α-Fe

Molecular dynamics simulations were performed to study the primary damage formation in α- Fe through collision cascades with a cascade energy of up to 100 keV. The pair analysis technique was introduced to characterize the spatial local structure distributions of atoms. The damaged microstructural unit characteristics of the body-centered cubic (bcc) crystal structure, as well as the number of point defects, followed a similar trend. Furthermore, the damaged atoms exist mostly in the microstructural characteristics of icosahedral and short-range ordering in amorphous states during and at the end of cascades. Most local spatial structures of the damaged atoms can be divided into two groups based on their corresponding non-characteristic index-pair change trends with time. The curves of the first group coincided with the vacancy (V) that exhibited one peak, whereas the curves of the second group exhibiting two peaks corresponded to the self-interstitial atoms (SIA). The maximum distance at which defects could interact with each other in space was the fifth nearest-neighbor distance of the atoms of perfect lattices in the bcc lattice. The number of local structural units of the damaged atoms that were connected with a single point defect (either V or SIA) continued to increase with increasing cascade energy by the end of the simulation. By contrast, the number of units that were connected with both V and SIA decreased. These results may help us understand the spatial configuration of atoms in the course of collision cascades.

A combinatorial procedure for finding isolating neighbourhoods and index pairs

SynopsisWe present a purely combinatorial procedure for finding an isolating neighbourhood and an index pair contained in a given set, being a finite union of cubes in Rs. It is applied for a computer-assisted computation of the Conley index of an isolated invariant subset of the Hénon attractor. As a corollary, it is shown that the Hénon attractor contains periodic orbits of all principal periods except for 3 and 5.

THE CONLEY INDEX AND GLOBAL BIFURCATIONS II.: ILLUSTRATIVE APPLICATIONS

This paper continues the presentation of a set of tools based on the Conley index for studying global dynamics and bifurcations. The first part gives the basic theory and some fundamental results. In this second part, we give a number of examples in more detail to illustrate the way these tools are applied. They are chosen to address issues such as: how is an index pair selected? how do we deal with high dimension? etc. In addition, we present powerful algebraic methods for computing the Conley index: the method of forming the cone over a space and the use of exact sequences and excision. It is understood that the likely users of these methods are far from being familiar with these mathematical results, so the emphasis is in revealing exactly how information is extracted from them. The many figures will hopefully aid the understanding of these novel concepts.