Hi Guido,
I'm afraid I don't understand the inner workings of the
TMA - I leave that to the brainiacs - Neo/Baluda et al.

I thought the same as you - the
TMA was analogous to the LWMA but it doesn't seem that way when plotted on a chart. The
TMA I
use has standard setting for period (20) & ATR (100 - although ATR doesn't make a huge difference) - fixed to D1 timeframe.
The LWMA uses 21 period zero shift but it is applied to the timeframe of the chart it is on - but as I
use D1 for looking at the cross then if
TMA (true) = LWMA then the lines should be almost the same but they are not.
So I can't really answer your question in terms of "why" but I can say they are not the same and I am currently > 2000 pips floating so I probably don't need to know the "why".
I would say to anyone looking at this method (
TMA/MA Cross) - don't just dive in when you see a cross - look at what has happened recently with this pair, the momentum of the cross etc. It is pretty basic but, for example, I haven't entered a trade on NZDUSD yet as the cross doesn't look that positive yet, price is just above the weekly pivot and BRN 0.8100, the H4
TMA is basically in range mode, the D1
TMA at the cross is around zero (not a good thing) AND if it does make a positive cross there will be plenty of opportunities to enter on a retracement.
GL.
Cheers,
Dave.
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