Developing of approaches for the unhomogeneus time series analysis based on statistical characteristics

Анна Александровна Чистякова


In this paper, a study of non-homogeneous time series, as a special case of a class of non-stationary time series, which are not given to stationary by integrating the 1st and 2nd order was carried out. Because of the presence of non-homogeneous components, time series is characterized by a non-linear trend, periodic components with variable amplitude, as well as a non-permanent structure. A method for identifying the series of this class based on statistical characteristics, using statistical tests and criteria was proposed. This method allows reasonable approach to selecting a method for forecasting a number of changes with respect to all the hidden features of the original data, as well as the reasons and assumptions of various forecasting methods. For example, in the construction of forecasting models of the non-homogeneous time series using statistical forecasting methods, such as AR (p), MA (q), ARMA (p, q), AR (p) + linear trend, ARCH (p), GARCH (p, q), SV (p), is inadequate in view of violating the requirements for applying these methods, in particular time invariance. An adaptive approach for forecasting non-homogeneous time series based on the method of singular spectrum analysis and presentation of time series in several phase spaces is proposed in the paper.

Another problem in forecasting the time series is a risk assessment in decision-making based on the forecasting model. A method for estimating the maximum level of losses in forecasting non-homogeneous time series with a given probability was developed in the paper. A confidence interval of forecasting non-homogeneous time series of exchange rates, which allows estimating the adoption of one or other solutions depending on the amount of the transaction was built.

The results obtained in this paper can be used for a sound approach to the selection of a forecasting method in automated systems, as well as in the evaluation of making management decisions.


non-homogeneous components; non-stationary time series; statistical characteristics; risk assessment; forecasting


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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061