Multivariate generalizations of the modified and adaptive time series correlation coefficients are obtained using the example of the dependence of currency pairs quotations and Brent crude oil price. The analysis of the movement of exchange rates and oil price in the R software environment. A much more detailed data analysis than the classical theory suggestion is obtained. Based on the identified trends in the dynamics of these markets, short-term forecasting was carried out using ARIMA, TBATS models and neural networks.

The work is devoted to identifying and tracking development trends, structural shifts in the economy under the influence of world markets, represented by non-stationary time series of gold, bitcoin and oil prices. The heuristic potential of the concept of the long and medium wave is used for forecasting purposes. The analysis of financial time series using the adaptive correlation coefficient is carried out. The dynamics of the traditional coefficient appears to be a significantly smoothed graph, which prevents sufficient qualitative analysis of the data. The results obtained are analysed to identify wave fluctuations, to determine the phases of growth, prosperity, recession and stagnation in the economy. An overview of the situation on the world markets for gold, bitcoin and oil based on the considered time series is presented. Based on the identified trends in the dynamics of these markets, short-term forecasting was carried out using ARIMA models and neural networks. The statistical calculations R environment is used.

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