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Franko,
A function[transformation] F is defined as linear when
F(x+y)=F(x)+F(y)
F(k*x)=k*f(x), k is a constant
The linearity of a function has nothing to do with coherence.
A simple example: The RSI transformation is obviously non-linear [do
not expect RSI(10*C)=10*RSI(C),
simply because 10*RSI(C) will vary from 0 to 1000.
On the other side, the RSI transformation should pass the c-test. To
avoid boring maths, simply
x=C;
y=10*C;
Plot(RSIA(x),"RSI[C]",4,1);
Plot(RSIA(y),"RSI[10*C]",1,1);
and you will see two identical plots.
BTW, the same definition implies that MACD is not a coherent
transformation, although it is pretty linear.
See the simple
x=C;
y=10*C;
MACDofx=EMA(x,12)-EMA(x,26);
MACDofy=EMA(y,12)-EMA(y,26);
MACDofxplusy=EMA(x+y,12)-EMA(x+y,26);
Plot(MACDofxplusy,"MACD of (x+y)",2,1);
Plot(MACDofx+MACDofy,"MACD of x +MACD of y",9,1);
Plot(MACDofy,"MACD of 10*x",1,1);Plot(10*MACDofx,"10*MACD of x",4,1);
to agree that MACD passes the linearity test,
although it does not pass the c-test [do not expect MACDofy and
MACDofy to have the same graph !!]
In practical terms, is there any limitation when we apply RSI or
MACD,
based on the fact that RSI is coherent and MACD is not ?
Dimitris Tsokakis
--- In amibroker@xxxxxxxxxxxxxxx, Franco Gornati <fgornati@xxxx>
wrote:
> MarkF2 wrote:
> > Fred- If you want simplistic, I'll give you simple and simpler :-)
> >
> > 1. Simple. Apply Eckhardt's c-Test for dimensional coherency:
> > "In essence, the c-test transforms relevant formulas in an
indicator
> > or system by multiplying every price term by a positive constant
c (c
> > not equal to 1), while leaving nonprice terms the same. If the
> > transformed indicator or system gives the same indications or
signals
> > as the original, then it has passed the c-test. If not, the
> > formulation in question is incoherent and depends unacceptably on
the
> > units chosen."
>
> Mark,
>
> put in mathematical terms it means that the indicator is a linear
function of Price.
>
> I = f(P) [I is the indicator]
>
> if f is linear
>
> f(a*P) = a*f(P) = a*I
>
> It means that the derived indicator a*I mimics in an amplified way
the indicator
> I but does not modify its behaviour. It would be different for non
linear relations.
>
> --
> Franco Gornati <fgornati@xxxx>
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