Excel-oriented calculator for financial flows stability diagnostics under batch data processing by chebyshev polynomials

Abstract

Purpose of work. Development of algorithms and software support of EXCEL-oriented methods for arraying of regression equations, using Chebyshev polynomials. Results. The work shows how aggravating geopolitical instability and effect of other pressure factors on the condition of economic systems in numerous countries leads to severe vulnerability of their financial systems. The result is slowing down of world economic growth, accelerated inflation pressure and business uncertainty. Under these circumstances the diagnostics of changes in directions, amounts, rates, regularity of business financial flows becomes quite important. Temporal variation of financial system influential parameters may be presented in the form of regression polynomials. In the present work Chebyshev polynomials were applied for their determination. This method was implemented in software products whose usage is limited by licensing restrictions. Therefore, the development of EXCEL-oriented software product applicable to formulation of regression equations using Chebyshev polynomials may be considered an urgent task. The work specifies calculation algorithms for Chebyshev regression polynomials up to fifth power inclusive, as well as transcribes block diagrams of their implementing algorithms. The determination of data packet, its index and data flows are also described. In order to compare the quality of Chebyshev polynomials in different powers a concept was introduced of relative error chain decilog. The work assumes that any discrepancy between indices of two adjacent flows means violation of process stability. The moment of stability violation corresponds to the highest number in pair of packets. Algorithm block diagram and numerical application example of our proposed method are shown.