Fisher Transform Indicator by Ehlers

Fisher Transform Indicator by Ehlers

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//  
// 	Market prices do not have a Gaussian probability density function
// 	as many traders think. Their probability curve is not bell-shaped.
// 	But trader can create a nearly Gaussian PDF for prices by normalizing
// 	them or creating a normalized indicator such as the relative strength
// 	index and applying the Fisher transform. Such a transformed output 
// 	creates the peak swings as relatively rare events.
// 	Fisher transform formula is: y = 0.5 * ln ((1+x)/(1-x))
// 	The sharp turning points of these peak swings clearly and unambiguously
// 	identify price reversals in a timely manner. 
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study(title="Fisher Transform Indicator by Ehlers Strategy", shorttitle="Fisher Transform Indicator by Ehlers")
Length = input(10, minval=1)
xHL2 = hl2
xMaxH = highest(xHL2, Length)
xMinL = lowest(xHL2,Length)
nValue1 = 0.33 * 2 * ((xHL2 - xMinL) / (xMaxH - xMinL) - 0.5) + 0.67 * nz(nValue1[1])
nValue2 = iff(nValue1 > .99,  .999,
	        iff(nValue1 < -.99, -.999, nValue1))
nFish = 0.5 * log((1 + nValue2) / (1 - nValue2)) + 0.5 * nz(nFish[1])
pos =	iff(nFish > nz(nFish[1]), 1,
	    iff(nFish < nz(nFish[1]), -1, nz(pos[1], 0))) 
barcolor(pos == -1 ? red: pos == 1 ? green : blue )
plot(nFish, color=green, title="Fisher")
plot(nz(nFish[1]), color=red, title="Trigger")