Notes on the MACD Enhanced Signal
The so called MACD Enhanced signal comes is based on Mathematical
Techniques in Financial Market Trading by Don K. Mak, World
Scientific Publishing, 2006, Chapter 4. This filter is described as
"Zerolag" EMA and is attributed to J.F. Ehlers. This filter is
most certainly not "zerolag", especially with the window sizes listed
here.
Although I have cited it here, I cannot recommend Don Mak's book. While Don Mak attempts to put
technical analysis on a more scientific and mathematical footing, the
book is needlessly obscure.
 M = window size
p_{t} is the tick price at time t
m is the EMA time series 
a = 2 / (M+1) Example: for M^{300}, a = 2 / (300 +1)
m_{t+1} = (a * p_{t} ) + (1  a) * m_{t}
If there is a series of tick prices p_{1}, p_{2}, p_{3}... how does the EMA start? Is it
m_{1} = (a * p_{2} ) + (1  a) * p_{1}
or, do we consider m_{0} = 0 and the equation is
m_{1} = (a * p_{2} ) + (1  a) * 0 ==> m_{1} = (a * p_{1} )
For m_{1}, I decided to treat m_{0} = 0.
The full MACD Enhanced is
S_{t} = m^{300}_{t}  m^{500}_{t}
Where m^{300} and m^{500} are the m EMA series with 300 and 500 element "windows".
X^{200}_{t+1} = ( a_{200} * S_{t} ) + (1  a) *X^{200}_{t}
Where a_{200} ==> a = 2/(200+1)
If we have the S time series S_{1}, S_{2}, S_{3}... how does the X^{200}_{t} series start. Is it
X^{200}_{1} = ( a_{200} * S_{2} ) + (1  a) *S_{1}
or, do we consider X_{0} = 0 and the equation is
X^{200}_{1} = ( a_{200} * S_{1} ) + (1  a) * 0 ==> X^{200}_{1} = ( a_{200} * S_{1} )
For X^{200}_{1} , I decided to treat X_{0} = 0.
