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Average of the next four bars, dropping off the last closing price C 1 gives

Average Price for Day 2=+++(C 5 C 4 C 3 C /4 2 )

And similarly for the next two days:

Average Price for Day 3=+++(C 6 C 5 C 4 C /4 3 )

Average Price for Day 4=+++(C 7 C 6 C 5 C /4 4 )

We now find the average of the averages for the first four days (Double
Smoothing):

=+++++++++++

++++

[( ) ( ) ( )

( )]

C C C C C C C C C C C C

C C C C

4 3 2 1 5 4 3 2 6 5 4 3

7 6 5 4 //16

=++++++[C 2C 3C 4C 3C 2C C /16 7 6 5 4 3 2 1 ]

Hence, we observe that the weighting for a triangular average is greater in
the middle of the period (i.e., 1−2−3−4−3−2−1). In order to construct a triangular
moving average, we need to first determine the period to be used.
Let us assume that we have identified a 19-period dominant cycle in the mar-
ket and we want to track it using a triangular moving average. We first find the
half-period value, which is given by (N + 1)/2 and rounding up if N is even. This
gives us (19 + 1)/2 = 10 periods. We shall now calculate the SMA of both averages
using this period. Hence, we use a 10-period triangular moving average to track
a 19-period cycle in the market. See Figure 11.9 for an example of the calcula-
tion for a 10-day triangular moving average. The last column on the right repre-
sents the moving average of the last 10 average prices on the CBOE Interest Rate
10-Year Treasury Note, beginning on May 29, 2009. Figure 11.10 is a plot of the
moving average.

(3) Linearly Weighted Moving average (WMa) A linearly weighted moving
average is also front weighted, meaning that it is more sensitive to recent prices,
which conveniently also reduces the impact of the drop-off effect. The weighting
factor is usually a series of reducing multiplication factors, the length of which
is equal to the period chosen. The more recent the prices or data, the larger will
be the weighting factor. An N-period weighted average is calculated as follows:

Weighted Average C=+−+−++[NNNN ( 1C) N− 1 ( 2 C) N− 2 ... ( ) ] [ (1C / 1 NN+ 1 )) ]/2

See Figure 11.11 for the calculation of the WMA.

(4) exponential Moving average (eMa) An exponential moving average
(EMA) is a front-weighted moving average. It is very sensitive to recent prices, and