Methods for Time Series Analysis Using Segmented Regression with Heteroskedasticity

The paper considers the problem of building and choosing the best mathematical model for describing the time series of the dependence of the airline's profit on the received revenue, taking into account the costs of aviation safety. The development of adequate forecasting models will make it possible to use available resources to achieve production goals of airlines while simultaneously solving aviation safety challenges. Several variants of approximation algorithms are considered. The first algorithm is based on the use of cluster analysis technologies. At the same time, visual analysis of the time series became a prerequisite for choosing three clusters for grouping data. A separate group linear approximation for each of the clusters made it possible to calculate the preliminary values of the abscissas of the breakpoint. The second approximation algorithm is based on the use of a three-segmented linear approximation. To find the optimal abscissa of the breakpoint, a three-dimensional optimization paraboloid was used. For the final approximation of the researched time series, the heteroskedasticity index was taken into account. The resulting final version of the approximation was used to solve forecasting problems.