by William Blau
A new twist on the venerable stochastic formula was presented in a January 1991 article,
"Double-smoothed stochastics," written by William Blau. Here, Blau expounds on stochastic double
smoothing in a somewhat different form that emphasizes momentum characteristics.
Double smoothing of both numerator and denominator of the original formula for %K of the stochastic
indicator aids in obtaining low-lag smooth-contoured indicator curves. In lieu of a single parameter to
specify the stochastic, the Ds-stochastic formulation provides an additional two parameters for a
double-EMA (exponential moving average) effect. The Ds-stochastic formula is given by:
where, for the numerator,
HH:q = highest high in a lookback of q-days
LL:q = lowest low in a lookback of q-days
Close-LL:q = numerator of Lane's q-day fast stochastic
Er(Close-LL:q) = r-day EMA of (Close - LL:q)
Es(Er(Close-LL:q)) =s-day EMA of Er (Close-LL:q)= double-smoothing
and, similarly, for the denominator.
Figure 1 depicts a train of high, low and close price bars. The dark bar on the right describes the range, HH:q- LL:q, assumed by the price bars in a lookback of q-bars. The raw stochastic formula,
Ds(q,1,1),represents where the current close is relative to the low point of the stochastic range. A close
near the upper portion of the range will be near the highest high in the most recent q-days, for example.
Figure 2 shows the same train of high, low and close price bars but with different annotations. The
stochastic range remains unchanged. The close is now referenced to the midpoint, 0.5 (HH:q + LL:q), of