• Journal of Intelligence and Information Systems
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• v.22 no.2
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• pp.115-125
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• 2016

The Bollinger Band indicating the current price position in the recent price action range is obtained by adding/substracting the simple standard deviation (SSD) to/from the simple moving average (SMA). In this paper, we first compare the characteristics of the SMA and the exponential moving average (EMA) in the operator's point of view. A basic equation is obtained between the interval length N of the SMA operator and the weighting factor ${\rho}$ of the EMA operator, that makes the centers of the 1st order momentums of each operator impulse respoinse identical. For equivalent N and ${\rho}$, frequency response examples are obtained and compared by using the discrete time Fourier transform. Based on observation that the SMA operator reacts more excessively than the EMA operator, we propose a novel exponential standard deviation (ESD) band centered at the EMA and derive an auto recursive formula for the proposed ESD band. Practical examples for the ESD band show that it has a smoother bound on the price action range than the Bollinger Band. Comparisons are also made for the gap corrected chart to show the advantageous feature of the ESD band even in the case of gap occurrence. Trading techniques developed for the Bollinger Band can be straight forwardly applied to those for the ESD band.