Wilder's average and the EMA are basically identical.

The only difference is the way that the smoothing constant of the EMA is calculated from the period.

For Wilder's average the smoothing constant is k = 1/n

For the EMA (as described by Jack K. Hutson in one of the early issues of the TASC magazine) a period of k = 2/(n+1) is used.

The advantage of the Hutson formula is that

- the EMA can be compared to a SMA with the same period
- that you can easily calculate higher timeframe EMAs by multiplying the period with the timeframe factor

Example: You can approximate an EMA(20) on an hourly chart with an EMA(80) calculated from 15 minute bars, but you cannot do this with Wilder's average.

Therefore today, all EMAs use the Hutson formula ( I call it Hutson formula, but in reality it is based on the single exponential model described in Robert G.Brown's "Smoothing, Forecasting and Prediction of Discrete Time Series, which was first published in 1963).

You do not need the modified ADX based on the EMA.

All you need to do is to adapt the period. Let us call the modified ADX "ADXmod". And now let us assume that you wish to display an ADXmod(21). Then you know that this indicator uses a smoothing constant of 2/(21+1) = 1/11. It is therefore identical with the ADX(11) of Wilder.

That said, you cannot approximate even periods of the ADXmod with the Wilder ADX, as it will not allow you to set the period to 10.5, although this is mathematically possible. If you wish, I will modify the NinjaTrader ADX to allow you to select broken periods.

The following 6 users say Thank You to Fat Tails for this post:

Actually, I was trying to get an ADX with the EMA reference in it to then substitute with the various MAs like HMA, ZELMA, T3, etc for experimentation =)

Something like the MACDplus in the forums where you can just swap the MA for the calculations part.

Like something of wikipedia,

So the idea is to change all the MAs used in calculations for +DI, -DI, ATR and ADX. =)

Azrael, did you ever succeed in achieving the ADX based on EMA.

Am coming from a forex background and tried Fat Tails advice of 2/(n+1) = 1/n but it hasnt helped.
FxPro has MT5 which has both types of ADX, I played around with the inputs but failed to get matches.

Please share it if you ever succeeded, this thread seems a dead horse but I will try.

Hi,
I've been trying to create this indicator (ADX using EMA) for Multicharts and the only helpfull information I've found is in this thread.
I take my hat off to Fat Tails for creating the Ninja version, I dont have ninja but been looking at Fat Tails code trying to reverse engineer and my head hurts

I wonder if Fat Tails or anyone else could help and look at the easylanguage code bellow (this is the standard DMI indicator in multicharts) and hint what values I'd need to change to calculate the ADX using EMA rather than Willder's avarage?
Thanks