Autoregressive - spectrally integrated moving average model
The class synthesis of mathematical models, based on sharing ideas of two methods, which in separate are viewed skeptically by many experts of the prediction field, is carried out. However, they are well substantiated theoretically. The first method is a deterministic method of different types of analysis and prediction, which has not been included in the standard mathematical software yet, i. e. the «Caterpillar»-SSA method. The second one is a statistical method, i. e. the Box-Jenkins method. The model of autoregression, namely spectrally integrated moving average, is proposed. This model implements a trend approach, which lies in modeling the process as a deviation of actual values of a relative trend component and leads to synergy, mutually compensating the opposite in nature disadvantages of its model components. The proposed ARSIMA model identifies the long-term process dependence only by two parameters. This model has a wide range of application.