ДЕКОМПОЗИЦІЯ МОДЕЛІ НЕСТАЦІОНАРНОГО ВИПАДКОВОГО ПРОЦЕСУ

Abstract

In the work, the peculiarity of the task of constructing the decomposition of a non-stationary model of a random process is studied using the examples of the analysis of two types of real data. The peculiarities of the decomposition of the model of a non-stationary random process are considered. It consists in the separate definition of an arbitrary trend, a seasonal component and a stationary component. This allows solving, for example, forecasting tasks. This task means several steps ahead in predicting the values of a random process. Some problems that arise when using the autoregression-integrated moving average (ARIMA) model for the decomposition of the model of a random non-stationary process are shown. The results of research on real data are given. They demonstrate the process of decomposition of a model of a non-stationary random process. The analyzed classes of random non-stationary processes with a trend allow us to solve two main problems with acceptable accuracy. The first task involves the decomposition of a model of a random non-stationary process. It includes the calculation of an arbitrary trend, a quasi-periodic seasonal component and a stationary component of the process. The second task involves the actual forecasting of a non-stationary time series using the ARIMA model. In the ARIMA model, it is assumed that the trends are deterministic and are linear, quadratic or higher order polynomials. The seasonal component is periodic and has equal counts in each period, which can be removed through the subtraction period. If the seasonal component does not satisfies these requirements, then when it is removed by difference operators, problems arise and the ARIMA model may lose accuracy.