There is in technical analysis an other price oscillator called relative strength index (RSI) that was introduced by J.W.Wilder and presented in 1978.(see MURPHY J.J.
Technical Analysis of the Futures Markets .New York Institute of Finance , chapter 10 p 295).
It is defined by the equation:
RSI in%=1-(100/(1+(sum of daily price units gained only in the upward days during the last k days )/( sum of daily price units lost only in the downward days during the last k days)))
Let us denote by D(x(n))=x(n)-x(n-1) then as the “sum of daily price units gained only in the upward days during the last k days”=sum of D(x(n)) for n=n-k to n, we rewrite it by simplifying the formula and we get an equivalent form. We put (Dx(n)-abs(Dx(n)))/2 and (Dx(n)+abs(Dx(n)))/2 for the price points gained in the nth down or up days respectively .Then with simplification on the quotients we get the next
We denote by x with bar the average of the signed price points gained in k-days (as are the smoothing days of the RSI) and by absolute value of x with a bar the average price points in absolute value gained in k days (Sometimes called the total variation of the curve over the resolution defined by the bars).
From this formula by noticing that (Average(|x|)+Average(x))/2 = Average(+x) , that is the average of the points gained only in the positive or up days, we may re-write iit as
RSI=Statisical_frequency_of_up_points =probability of an up-tick (over the resolution defined by the bars).
Another way to re-write it is:
From this formula by noticing that (Average(|x|)+Average(x))/2 = Average(+x) , that is the average of the points gained only in the positive or up days, we may re-write iit as
RSI=Statisical_frequency_of_up_points =probability of an up-tick (over the resolution defined by the bars).
Another way to re-write it is:
For normal random variables it holds that
thus the RSI becomes a simple formula of the inverse of the coefficient of variation or Sharpe ratio.
From this we deduce that this oscillator and its success is not accidental but is related to a well known and very useful coefficient in statistics.
The statistical quantities need to me measured in the front-office of the trading are the price position in the channel around the average, the velocity (1st derivative) and the acceleration-deceleration (2nd derivative), which is done as statistical quantities by a hypothesis test or confidence interval. The support-resistance levels can be measured also by action-volume histograms. The measurements are done with convenient indicators, and can also define in a statistically valid way, not only , the channels , and Eliot-waves but also the spikes.
The statistical quantities need to me measured in the front-office of the trading are the price position in the channel around the average, the velocity (1st derivative) and the acceleration-deceleration (2nd derivative), which is done as statistical quantities by a hypothesis test or confidence interval. The support-resistance levels can be measured also by action-volume histograms. The measurements are done with convenient indicators, and can also define in a statistically valid way, not only , the channels , and Eliot-waves but also the spikes.
