Whitening filter and innovational representation of fractional Brownian motion

In this paper, by means of fractional differential–integral technique we give a new whitening filter formula for fractional Brownian motion defined by Mandelbrot and van Ness Mandelbrot BB, van Ness JW. SIAM Rev 1968;10(4):422]. This new formula has potential use in time series analysis and in detecting signals as Barton and Vincent Poor Barton RJ, Vincent Poor H. IEEE Trans Inform Theory 1988;34(5):943] have shown. Another potential application of it is behavioral finance, where the arbitrage opportunities that come from the reversal effect of stock returns, can be eliminated by such a formula.