A LINEAR APPROXIMATION METHOD IN PREDICTION OF CHAOTIC TIME SERIES
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The basic problem of scientific investigation is forecasting - How can we predict the future, given the past? The behaviour of periodical structure we can predict in infinity, but chaotic structure is predictable in the short term only. It is connected with a basic property - the sensitivity on initial conditions. It consists in that very similar initial conditions sometimes give very different structure's behaviour. The reason for this is that we can establish initial conditions with finished exactitude, but miscalculations grow exponentially. This means that when we want to predict the behaviour of such a structure in any moment, we would dispose of the data entrance passed with infinite exactitude as well as execute all calculation with finite accuracy. Otherwise, small mistakes in setting initial values as well as miscalculations grow in an exponential way. This means that the evolution of such systems is very complex and virtually unpredictable in the long-term. There exist different methods of forecasting a chaotic time series. This article presents a method of the linear approximation applied to a short-term prediction regarding the share prices on the Warsaw Stock Exchange. The time series of share prices is a type of deterministic series and can behave chaotically.
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