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Arun DTMA by Preston Umrysh

The following formula is for plotting a 10-period tema moving average:


How does one derive this formula?

Looking at the derivation of a Zero Lag EMA, I have proceeded as follows but I don't get the above formula. I know I'm wrong somewhere.


Please correct me.





A tema is simply a triple smoothed EMA. It would simply be

A DEMA is simply a double smoothed EMA or

Your formula is 3 times an EMA - 3 times a DEMA which could be
simplified to the difference of an EMA-DEMA plus a TEMA

Hope this helps,




Finally had some time to put together some information for you on the indicator that you requested.

Important to remember that the TEMA and the DEMA were both developed by Patrick Mulloy. They both use unique methods to determine their final values. I believe the following information explains everything.

DEMA and TEMA are unique smoothing indicators developed by Patrick Mulloy. TEMA was originally introduced in the January 1994 issue of Technical Analysis of Stocks & Commodities magazine. As Mr. Mulloy explains in the article:

"Moving averages have a detrimental lag time that increases as the moving average length increases. The solution is a modified version of exponential smoothing with less lag time." TEMA is an acronym that stands for Triple Exponential Moving Average. HOWEVER, the name of this smoothing technique is a bit misleading in that it is not simply a moving average of a moving average of a moving average. It is a unique composite of a single exponential moving average, a double exponential moving average, and a triple exponential moving average that provides less lag than either of the three components individually.


{Plots either a DEMA or TEMA}
Plot:= Input("Display [1] Dema[2] Tema",1,2,2);
Period:= Input("What Period",1,250,10);
EMA1:= Mov(C,Period,E);
EMA2:= Mov(EMA1,Period,E);
EMA3:= Mov(EMA2,Period,E);
Difference:= EMA1 - EMA2;
DMA:= EMA1 + Difference;


Hope this helps,



Another reference is William Blau, 'Momentum, Direction and Divergence', where Blau applies double smoothing to a variety of indicators. I'm not sure who had the idea first.




Good point. I checked the date on Blau's book and found it was published in March of 1995. So both authors were in the same timeframe. The obvious next question would be whether Blau and Mulloy used the same methods.

I checked two of Blau's indicators, the ergotic and true strength, and found them using the simple moving of the moving method. This is assuming that the indicator formulas that I have are written correctly.

Mulloy on the other hand uses a "unique composite" method to supposedly reduce the lag time. I thought that was interesting enough to not only answer the original question that Arun had but also point out the differences.

Either way it looks like the middle 90's were an interesting period of time when it comes to the methods that people were using to smooth their moving averages.

Thanks for your insight,



Hi Preston,

Thanks for your help on Tema moving average. Actually, I had plotted a 10 period Zero Lag exponential moving average on a chart and then plotted Metastock's 10 period Dema on the same chart and Dema plotted right on top of Zero Lag ma, so I concluded that both are same. Since then I was wondering about the full derivation of Tema because Metastock doesn't give the full formula. Thanks again


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