This scientific work is dedicated to applying of two-layer interval weighted graphs in non-stationary time series forecasting and evaluation of market risks. The first layer of the graph, formed with the primary system training, displays potential system fluctuations at the time of system training. Interval vertexes of the second layer of the graph (the superstructure of the first layer) which display the degree of time series modeling error are connected with the first layer by edges. The proposed model has been approved by the 90-day forecast of steel billets. The average forecast error amounts 2,6% (it’s less than the average forecast error of the autoregression models).
In this paper we propose a method for predicting significant multivariate nonstationary time series, ie series, in which changes in the structure, variables, or model coefficients of the variables. Due to the time-dependent processes that give rise to economic indicators, most economic time series falls into the category under consideration. The need to predict rate of capital flight as the subject of investigation, the volume of Russian investment abroad of non-banking corporations, as its major component.
The current work is devoted to study of interrelations of the obtained time series by means of econometric and wavelet analysis. At the first stage of this study, econometric analysis was conducted, regression was constructed. In the regression influence of the number of nomads and the amount of resource on the number of plowmen was studied. The coefficient of determination (R2) of the constructed regression turned out to be 0.81, the Durbin-Watson statistics equals to 0.94, which indicates the presence of positive first-order autocorrelation of errors. The next stage is an analysis based on wavelet transforms, which helps to get rid of high-frequency "noise" and interference in considered time series. Within the framework of this paper, the Haar wavelet and the Daubechies 2 tap wavelet were considered (the remaining wavelets give similar results). After the time series had been cleared by the wavelet analysis, regression analysis was applied again. The coefficient of determination of new regressions depending on which wavelet was applied and the interference of what frequency were removed took values in the range from 0.86 to 0.93. The coefficient of determination of new regressions depends on which wavelet was applied and the interference of what frequency were removed. It takes values in the range from 0.86 to 0.93. However, the Durbin-Watson statistics decreased its values and began to take values in the range from 0.01 to 0.46, which still indicates the presence of positive first-order autocorrelation of errors. In the end, we learn that in this situation, the application of wavelet analysis significantly increases the explanatory power of regression, on the other hand, the problem of autocorrelation of errors can not be resolved in this way, in some sense it is only getting worse.