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A new, non-statistical method is presented for analysis of the past history and current evolution of economic and financial processes. The method is based on the sliding model approach using linear differential or difference equations applied to discrete information in the form of known chronological data (time series) about the process. An algorithm is proposed that allows one to project the current evolution of the process onto some period of its future development. Computer code in visual basic is developed that has been validated in application to American stock index S&P 500, with predicted values within 5% of real data over long periods of the recent past history. The algorithm and the code can be applied to practical problems in finance and economy in time of its normal evolution without catastrophic events.