Intraday Trading : EMA, MacD Enhanced and other Strange Non-linear Functions
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 "Zero-lag" EMA and is attributed to J.F. Ehlers. This filter is most certainly not "zero-lag", 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.
If there is a series of tick prices p1, p2, p3... how does the EMA start? Is it
or, do we consider m0 = 0 and the equation is
For m1, I decided to treat m0 = 0.
The full MACD Enhanced is
If we have the S time series S1, S2, S3... how does the X200t series start. Is it
or, do we consider X0 = 0 and the equation is
For X2001 , I decided to treat X0 = 0.