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Time Series Analysis

In recent years a powerful technique of time series analysis has been developed and applied to many practical problems. This technique is based on the use of the Singular-value decomposition of the so-called trajectory matrix obtained from the initial time series by the method of delays. It is aimed at an expansion of the original time series into a sum of a small number of 'independent' and 'interpretable' components. Also, the spatial analogies of the popular ARMA type stochastic time series have been developed based on the fractional generalizations of the Laplacian with two fractal indices. These models describe important features of processes of anomalous diffusions such as strong dependence and/or intermittency.