The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.