Identification and accounting of aperiodic anomalies in dynamic series with cyclic components

Abstract

This article is devoted to solving the problem of studying dynamic series with aperiodic point anomalous changes in the values of levels arising from the influence of socio-economic and/or external and/or internal political factors on the simulated object or system. It is assumed that there are sufficient grounds to believe that the series contain a cyclic component (for example, if seasonal changes in the behavior of the simulated object or system are clearly expressed). The use of classical mathematical methods, as a rule, leads to obtaining models that do not allow describing and predicting their values with acceptable accuracy due to the presence of abnormal changes in the levels of the series. The article develops methods for modeling dynamic series with this feature, based on the identification and exclusion of abnormal changes in the values of the series levels. For this purpose, the anomalous values of the levels are proposed to be divided into structural, changing the polarity (i.e., the direction of change) of the cyclic component, and parametric, preserving the polarity, but significantly changing the absolute value of the level of the series. To identify point structural anomalies, an indicator method has been developed, and the identification of point parametric anomalies is based on the assumption of the normality of the law of the distribution of values of the cyclic component with point exceptions of the series levels. To solve the problem, the cyclic and trend components for additive and multiplicative models of the series were identified at intervals of non-anomalous changes in the values of levels in the interests of predicting future values of the series. A numerical example is given confirming the high efficiency of the developed methods.