Time series interpolation and application of its methods in financial analysis

In the modern market economy conditions, financial information is very significant when evaluating the results of enterprises’ financial status and activity results. General economic, mathematical, heuristic methods are used for this type of analysis. The article analyses application opportunities for one of the mathematical research methods–time series–as well as its research instruments, discusses the place and role of interpolation methods in a financial analysis. The article reveals that interpolation methods which may be used to determined former values of an enterprise’s financial indicators or identify reasons which determined the enterprise’s financial status and activity results are the following: 1) graphic and arithmetic interpolation in a linear equation; 2) geometric interpolation based on the compound percentage formula and 3) interpolation by averaging.

A Comparative Study of Interpolation Schemes in Overset Meshes for the PLIC-VOF Method in Multiphase Flows

Piecewise Linear Interface Calculation (PLIC) schemes have been extensively employed in the Volume-of-Fluid (VOF) method for interface capturing in numerical simulations of multiphase flows. Dynamic overset meshes can be especially useful in applications involving component motions and complex geometric shapes. The basic idea of the overset mesh is the variable field interpolation within the overlapped region between the background and body meshes. The acceptor cell value is evaluated by a weighted average of its donors. The weighting factors are calculated by different algebraic methods, such as the averageValue, injection and inverseDistance schemes, which are implanted in the foam-extend library. A geometric interpolation scheme of the VOF field in overset meshes for the PLIC-VOF method has been proposed in the present study. The VOF value of an acceptor cell is evaluated geometrically with the reconstructed interfaces from the corresponding donor elements. Test cases of advecting liquid columns of different shapes inside a unit square/cube with a prescribed rotational velocity field have been performed to demonstrate the accuracy of the proposed overset interpolation scheme by comparing it with three algebraic ones. The proposed scheme has been shown to yield higher accuracy.

Enhanced Fully Generalized Spatial Modulation for the Internet of Underwater Things

A full design of the Internet of Underwater Things (IoUT) with a high data rate is one of the greatest underwater communication difficulties due to the unavailability of a sustainable power source for the battery supplies of sensor nodes, electromagnetic spread weakness, and limited acoustic waves channel bandwidth. This paper presents a new energy-efficient communication scheme named Enhanced Fully Generalized Spatial Modulation (EFGSM) for the underwater acoustic channel, where the different number of active antennas used in Fully Generalized Spatial Modulation (FGSM) is combined with multiple signal constellations. The proposed EFGSM enhances energy efficiency over conventional schemes such as spatial modulation, generalized spatial modulation, and FGSM. In order to increase energy and spectral performance, the proposed technique conveys data bits not just by the number of active antenna's index as in the existing traditional FGSM, but also using the type of signal constellation to increase the data bit rate and improve power saving without increasing the receiver’s complexity. The proposed EFGSM uses primary and secondary constellations as indexes to carry information, they are derived from others by geometric interpolation signal space. The performance of the suggested EFGSM is estimated and demonstrated through Monte Carlo simulation over an underwater acoustic channel. The simulation results confirm the advantage of the suggested EFGSM scheme not just regarding energy and spectral efficiency but also concerning the average bit error rate (ABER).

Spatial interpolation of point velocities in stream cross-section

The most frequently used instrument for measuring velocity distribution in the cross-section of small rivers is the propeller-type current meter. Output of measuring using this instrument is point data of a tiny bulk. Spatial interpolation of measured data should produce a dense velocity profile, which is not available from the measuring itself. This paper describes the preparation of interpolation models. Measuring campaign was realized to obtain operational data. It took place on real streams with different velocity distributions. Seven data sets were obtained from four cross-sections varying in the number of measuring points, 24-82. Following methods of interpolation of the data were used in the same context: methods of geometric interpolation arithmetic mean and inverse distance weighted, the method of fitting the trend to the data thin-plate spline and the geostatistical method of ordinary kriging. Calibration of interpolation models carried out in the computational program Scilab is presented. The models were tested with error criteria by cross-validation. Ordinary kriging was proposed to be the most suitable interpolation method, giving the lowest values of used error criteria among the rest of the interpolation methods.