COMPARATIVE ANALYSIS OF TWO METHODS FOR TAKING INTO ACCOUNT HETEROSKEDASTICITY DURING MATHEMATICAL MODELS BUILDING - Kuzmin, Valeriyi; Zaliskyi, Maksym; Petrova, Yuliia; Cheked, Igor (Science-based technologies, 2019)
The article deals with the problem of comparative analysis of two methods of taking into account heteroskedasticity during mathematical models building. Heteroskedasticity accounting is a new trend for the empirical data analysis. Heteroskedasticity is characterized by different values of variance for data in one sample. The presence of heteroskedasticity can lead to approximation accuracy decreasing in case of ordinary least squares method utilization. Therefore, this article concentrates on the problem of heteroskedasticity accounting in case of empirical data analysis. The first step during the mathematical model building is to approximate the data using the ordinary least squares method. In this case, the approximation function is pre-selected in advance based on visual analysis of the statistical data structure. The next step in mathematical model building is to take into account heteroscedasticity. There are different tests for heteroskedasticity detection. This article discusses the direct method of the heteroskedasticity equation construction and the new method that is compared with the direct one. The direct method is based on the calculation of average values and standard deviations for in each section of initial sample. Heteroskedasticity weighting coefficients are calculated according to the approximation of standard deviations dependence on the average values for statistics using a linear function. This method has a significant weakness: it requires multiple measurements for each sample section. During solving the problems of synthesizing a new algorithm for heteroskedasticity detecting and accounting, the authors propose a new quantitative measure of heteroskedasticity. The estimation of the proposed heteroskedasticity index is performed in the following sequence: 1) for several options of possible values of the heteroskedasticity index, the corresponding approximation functions are calculated; 2) the sum of squared deviations is calculated for each obtained function; 3) the heteroskedasticity index is equal to value for which the sum of squared deviations is minimal. A unique example of empirical data with multiple measurements in each section is considered. The analysis of such data allowed justifying the reliability and adequacy of the new method for heteroskedasticity detecting and accounting. The new method of heteroskedasticity accounting allows us to construct the mathematical model without carrying out multiple expensive measurements in each section.