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--- In amibroker@xxxxxxxxxxxxxxx, "Tomasz Janeczko" <amibroker@xxxx>
wrote:
> Dimitris,
>
>
> > >
> > > Not really. By definition DEMA and all exponential moving
averages
> > because of their recursive formula,
> > > require only 2 (EMA) or 3 bars (DEMA/TEMA) to calculate first
value.
> > > But it just the convention that first 2 * len periods are being
> > considered as "not accurate".
> >
> > Tomasz,
> > OK for the first 2*len periods. Is it accurate for the next 2*len
> > periods?
> > Is it accurate for the next 4*len periods ?
> > What is accurate for you ? 10% divergence, 1% divergence, 0.01%
> > divergence ?
> > If the final amibroker use is to trade, a cross(X,20) is *very
> > different* from a cross(X,21) in a [15, 40] scale.
>
> Please see the reply I have just sent to your other post.
> Because of the fact that EMA and DEMA are INITIALIZED differently
> it needs 2 * len bars for DEMA re-implemented using EMA
> to converge with built-in DEMA.
> After this initial stage they are the same.
Tomasz,
for len=200 your explanation means that after the 400th bar built-in
DEMA and EMA-equivalent "are the same.
Did I understand well ?
In my gifs there is no match after the 400th bar.
Do we see the same gifs ?
Dimitris Tsokakis
>
> As Fred wisely pointed out AMA-reimplemented DEMA is the same
> from the start because it is initialized the same way as DEMA.
> (Initial value is the first value of input array).
>
> As you probably know all exponential-smoothers are recursive.
> It means that they take one (or more) previous value(s) of itself
> to calculate todays value.
> EMA is simply
>
> factor = 2 / ( periods + 1 );
>
> EMA( today ) = ARRAY( today ) * factor + (1 - factor ) * EMA(
yesterday ).
>
> This EMA( yesterday) is just previous value of EMA.
> So we have go recurrency here.
> The problem is that at BAR ZERO you don't have any PREVIOUS value.
> You have to initialize somehow.
>
> One approach is to use ARRAY( 0 ) as initial value of EMA
>
> EMA( 0 ) = ARRAY( 0 )
>
> This approach is used by DEMA, TEMA, AMA, AMA2
>
> Second approach is to initialize EMA( periods ) by simple moving
average
> and start calculations from periods + 1:
>
> for all bar < periods EMA( bar ) = NULL
>
> EMA( periods ) = MA( periods )
>
> for all bars > periods
> EMA( bar ) = ARRAY( bar ) * factor + (1 - factor ) * EMA( bar - 1 ).
>
> In English: at bar = periods we initialize EMA with simple moving
average value because
> it is not recurrent. Then we continue usual EMA recursive
calculation.
>
> This method is used by EMA to match Metastock way of calculation
of EMA
> (requested by numerous users)
>
> Best regards,
> Tomasz Janeczko
> amibroker.com
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