Computational intelligence in time series forecasting : by Ajoy K. Palit;Dobrivoje Popovic

By Ajoy K. Palit;Dobrivoje Popovic

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Extra info for Computational intelligence in time series forecasting : theory and engineering applications

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E. they can be represented by the values that may be randomly repeated several times without maintaining any definite periodicity. 5 dx dt `, 2 which is sensitive to its initial conditions. This can be presented geometrically by the trajectory of the system in the phase plane, in which the trajectory of nondissipative systems make up a set of nested closed curves, whereas those of dissipative nonlinear systems for all initial conditions lead to trajectories that either lie on a single surface or converge to individual points in phase space.

They are chaotic, characterized by values that appear to be randomly distributed and non-periodic, but are actually resulting from a completely deterministic process. e. they can be represented by the values that may be randomly repeated several times without maintaining any definite periodicity. 5 dx dt `, 2 which is sensitive to its initial conditions. This can be presented geometrically by the trajectory of the system in the phase plane, in which the trajectory of nondissipative systems make up a set of nested closed curves, whereas those of dissipative nonlinear systems for all initial conditions lead to trajectories that either lie on a single surface or converge to individual points in phase space.

5. In this case I( f ) is referred to as the sample spectrum. , X n )T T (a0 , a, b) and ª1 cos Z sin Z º « » «1 cos 2Z sin 2Z » ». A= « «... .... » « » ¬«1 cos nZ sin nZ »¼ Minimizing the least-squares n 2 ¦ ( X t  a0  a cos Z t  b sin Z t ) t 1 the ș can be estimated using the pseudo inverse relation Tˆ ( AT A) 1 AT X . In order to use the spectral expansion technique for forecasting purposes, we need first to observe the given time series carefully to check whether it contains any trend and/or seasonality.

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