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On the Linear Relation of Signals

EDI CAHYONO
In this paper two signals over finite and closed interval of time are considered. A linear relation of the two with shifting is defined. In general, when a signal is expressed linearly of another with shifting, this gives an error. The absolute error should be minimized to have the best approximation. For the case of discrete signals without shifting, minimizing this error is just the well-known least square method. Hence, the proposed relation of signals is a generalization of the least square method. Criterion of approximating a signal linearly of the other is based on the relative error. The relative error is defined by comparing the norm of absolute error with the norm of the normalized approximated signal. Geometric interpretation and the applications in finance are also discussed. Especially in finance, the relation of signals can be applied to predict the dynamics of stocks, exchange rates and commodity prices. Predicting such dynamics on itself is very difficult, especially for high frequency data. Key-Words: - Relation of signals, Norm, Relative error, Dynamics of stocks, exchange rates, Commodity prices

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Diterbitkan pada: WSEAS TRANSACTIONS on SIGNAL PROCESSING Vol. 10, Th 2014 E-ISSN: 2224-3488

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