Evaluation of similarity of trend functions

Abstract

An approach to the evaluation of the similarity of the functions - approximating trend is proposed. The evaluation process consists of two stages: approximation techniques specific to non-linear regressions are applied, then certain procedures are used - algorithms for comparing the trend-functions obtained. Approximating functions are made up of components of polynomial form as well as terms - parameterized trigonometric functions sine and cosine. A function of this form allows us to obtain approximating functions at an acceptable level of accuracy for each individual case. Beforehand, the primary data sets are subjected to a smoothing process, which also provides for the inclusion of some parameters for the purposes of qualitative monitoring of operations to exclude exceptional values, values that, in some cases, can have a significantly negative impact. Varying the parameters of the approximating functions, in particular, of the trigonometric functions, can provide us with an approximation at a proper level of precision. In some cases, a high level of approximation accuracy can also have a negative impact. Having already obtained the trend functions for the respective data sets, we continue with the process of calculating the parameters that determine the basic fundamental properties of the obtained trend functions. For this purpose, the techniques of researching functions according to theories in the field of applied mathematics are used. Then, the domain of the independent variable is to be divided into several intervals, not necessarily of the same length, then, for each of them, the values corresponding to monotony effects, inflection points, extremes, etc. are calculated. The obtained values are to be included in the distance calculation formula. CZU: 004.421.2;JEL: C63, I21, I23, I25, I29; DOI: https://doi.org/10.53486/cike2022.37