Can anyone code John Ehler's FRAMA ?

This topic has 13 replies, 4 voices, and was last updated 7 years ago by Bard.

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11/24/2016 at 2:11 PM #17097

Bard

I was looking into Ehlers Cycle theories and came across a Moving Averages Study that shows Ehler’s Fractal Adaptive Moving Average (FRAMA) is far superior to the EMA and SMA (although I don’t know how it would stand up to Kaufman’s Adaptive Moving Average) :

http://etfhq.com/blog/2010/10/09/frama-is-it-effective/#Best

Does anyone know how to code it from this Metatrader code? :

https://www.mql5.com/en/code/72

Cheers
Brad

Bard

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11/24/2016 at 2:40 PM #17102

Nicolas

Found this old code on a German forum for FRAMA moving average , modified some variables names for recent PRT version :

// FRAMA

p = 20

pri=Customclose
len=p


N3=(Highest[len](High)-Lowest[len](Low))/len

mH=High
L=Low

For count=0 To len/2-1
If High[count] > mH Then
mH=High[count]
Endif

If Low[count] < L Then
L=Low[count]
Endif
Next

N1=(mH-L)/(len/2)

HH=High[len/2]
LL=Low[len/2]

For count=len/2 To len-1
If High[count] > HH Then
HH=High[count]
Endif

If Low[count] < LL Then
LL=Low[count]
Endif
Next

N2=(HH-LL)/(len/2)

If N1 > 0 And N2 > 0 And N3 > 0 Then
Dimen=(Log(N1+N2)-Log(N3))/Log(2)
Endif

alpha=Exp(-4.6*(Dimen-1))

If alpha < 0.01 Then
alpha=0.01
Endif

If alpha > 1 Then
alpha=1
Endif

Filt=alpha*pri+(1-alpha)*Filt[1]

If Barindex < len+1 Then
Filt=pri
Endif

Return Filt as "FRAMA"

// FRAMA

p = 20

pri=Customclose

len=p

N3=(Highest[len](High)-Lowest[len](Low))/len

mH=High

L=Low

For count=0 To len/2-1

If High[count] > mH Then

mH=High[count]

Endif

If Low[count] < L Then

L=Low[count]

Endif

N1=(mH-L)/(len/2)

HH=High[len/2]

LL=Low[len/2]

For count=len/2 To len-1

If High[count] > HH Then

HH=High[count]

Endif

If Low[count] < LL Then

LL=Low[count]

Endif

N2=(HH-LL)/(len/2)

If N1 > 0 And N2 > 0 And N3 > 0 Then

Dimen=(Log(N1+N2)-Log(N3))/Log(2)

Endif

alpha=Exp(-4.6*(Dimen-1))

If alpha < 0.01 Then

alpha=0.01

Endif

If alpha > 1 Then

alpha=1

Endif

Filt=alpha*pri+(1-alpha)*Filt[1]

If Barindex < len+1 Then

Filt=pri

Endif

Return Filt as "FRAMA"

I’ll post it too into the Library with credits for the author of course.

1 user thanked author for this post.

Bard

Nicolas

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11/24/2016 at 3:04 PM #17108

Nicolas

Added to the Library for future reference: FRAMA indicator download

Nicolas

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11/24/2016 at 4:23 PM #17116

Bard

Thanks Nicolas, much appreciated.

Do you know if FRAMA is meant to have a fast (FC) and slow (SC) moving average setting like the Kaufman Adaptive Mov Ave?
On the link above (efthq blog) is mentions in it’s conclusion:

“The FRAMA is astoundingly effective as both a fast and a slow moving average and will outperform any SMA or EMA. We selected a modified FRAMA with a “FC” of 4, a “SC” of 300 and a “FRAMA” period of 126 as being the most effective fast FRAMA although the settings for a standard FRAMA will also produce excellent results. For a slower or longer term average the best results are likely to come from a “FC” of 40, a “SC” of 250 and a “FRAMA” period of 252.”

Cheers

Brad

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12/05/2016 at 7:36 PM #17842

Bard

Hi Nicolas,

The code above does appear to be come from a paper written by Ehler’s: http://www.mesasoftware.com/papers/FRAMA.pdf
But I think there is a newer version. I found this code below for Ehler’s FRAMA which has the fast and slow moving averages setting.

#'FRactal Adaptive Moving Average
#'@param HLC an HLC price series
#'@param n a lookback period
#'@param FC a fast constant--aka lowest n for an EMA
#'@param SC a slow constant--aka lowest n for an EMA
#'@param triggerLag a number of days by which to lag the original computation
#'@return an xts containing the FRAMA and the trigger
#'@references 
#'\cr\url{http://www.mesasoftware.com/Papers/FRAMA.pdf}
#'\cr\url{http://etfhq.com/blog/2010/09/30/fractal-adaptive-moving-average-frama/}
#'@export
"FRAMA" <- function(HLC, n=20, FC=1, SC=200, triggerLag=1, ...) {
  price <- ehlersPriceMethod(HLC, ...)
  if (n%%2==1) n=n-1 #n must be even
  N3 <- (runMax(Hi(HLC), n)-runMin(Lo(HLC), n))/n
  N1 <- (runMax(Hi(HLC), n/2)-runMin(Lo(HLC), n/2))/(n/2)
  lagSeries <- lag(HLC, n/2)
  N2 <- (runMax(Hi(lagSeries), n/2)-runMin(Lo(lagSeries), n/2))/(n/2)
  dimen <- (log(N1+N2)-log(N3))/log(2)
  w <- log(2/(SC+1))
  oldAlpha <- exp(w*(dimen-1))
  oldN <- (2-oldAlpha)/oldAlpha
  newN <- ((SC-FC)*(oldN-1)/(SC-1))+FC
  alpha <- 2/(newN+1)
  alpha[which(alpha > 1)] <- 1
  alpha[which(alpha < w)] <- w
  alphaComplement <- 1-alpha
  initializationIndex <- index(alpha[is.na(alpha)])
  alpha[is.na(alpha)] <- 1; alphaComplement[is.na(alphaComplement)] <- 0
  FRAMA <- rep(0, length(price))
  FRAMA[1] <- price[1]
  FRAMA <- computeFRAMA(alpha, alphaComplement, FRAMA, price)
  FRAMA <- xts(FRAMA, order.by=index(price))
  FRAMA[initializationIndex] <- alpha[initializationIndex] <- NA
  trigger <- lag(FRAMA, triggerLag)
  out <- cbind(FRAMA=FRAMA, trigger=trigger)
  return(out)
}

#'FRactal Adaptive Moving Average

#'@param HLC an HLC price series

#'@param n a lookback period

#'@param FC a fast constant--aka lowest n for an EMA

#'@param SC a slow constant--aka lowest n for an EMA

#'@param triggerLag a number of days by which to lag the original computation

#'@return an xts containing the FRAMA and the trigger

#'@references

#'\cr\url{http://www.mesasoftware.com/Papers/FRAMA.pdf}

#'\cr\url{http://etfhq.com/blog/2010/09/30/fractal-adaptive-moving-average-frama/}

#'@export

"FRAMA" <- function(HLC, n=20, FC=1, SC=200, triggerLag=1, ...) {

price <- ehlersPriceMethod(HLC, ...)

if (n%%2==1) n=n-1 #n must be even

N3 <- (runMax(Hi(HLC), n)-runMin(Lo(HLC), n))/n

N1 <- (runMax(Hi(HLC), n/2)-runMin(Lo(HLC), n/2))/(n/2)

lagSeries <- lag(HLC, n/2)

N2 <- (runMax(Hi(lagSeries), n/2)-runMin(Lo(lagSeries), n/2))/(n/2)

dimen <- (log(N1+N2)-log(N3))/log(2)

w <- log(2/(SC+1))

oldAlpha <- exp(w*(dimen-1))

oldN <- (2-oldAlpha)/oldAlpha

newN <- ((SC-FC)*(oldN-1)/(SC-1))+FC

alpha <- 2/(newN+1)

alpha[which(alpha > 1)] <- 1

alpha[which(alpha < w)] <- w

alphaComplement <- 1-alpha

initializationIndex <- index(alpha[is.na(alpha)])

alpha[is.na(alpha)] <- 1; alphaComplement[is.na(alphaComplement)] <- 0

FRAMA <- rep(0, length(price))

FRAMA[1] <- price[1]

FRAMA <- computeFRAMA(alpha, alphaComplement, FRAMA, price)

FRAMA <- xts(FRAMA, order.by=index(price))

FRAMA[initializationIndex] <- alpha[initializationIndex] <- NA

trigger <- lag(FRAMA, triggerLag)

out <- cbind(FRAMA=FRAMA, trigger=trigger)

return(out)

}

There is also metatrader code using log values of the EMA: https://www.mql5.com/en/code/72

FRAMA(i) = A(i) * Price(i) + (1 - A(i)) * FRAMA(i-1)
where:

FRAMA(i) - current value of FRAMA;
Price(i) - current price;
FRAMA(i-1) - previous value of FRAMA;
A(i) - current factor of exponential smoothing.
Exponential smoothing factor is calculated according to the below formula:

A(i) = EXP(-4.6 * (D(i) - 1))
where:

D(i) - current fractal dimension;
EXP() - mathematical function of exponent.
Fractal dimension of a straight line is equal to one. It is seen from the formula that if D = 1, then A = EXP(-4.6 *(1-1)) = EXP(0) = 1. Thus if price changes in straight lines, exponential smoothing is not used, because in such a case the formula looks like this:

FRAMA(i) = 1 * Price(i) + (1 - i) * FRAMA(i-1) = Price(i)
I.e. the indicator exactly follows the price.

The fractal dimension of a plane is equal to two. From the formula we get that if D = 2, then the smoothing factor A = EXP(-4.6*(2-1)) = EXP(-4.6) = 0.01. Such a small value of the exponential smoothing factor is obtained at moments when price makes a strong saw-toothed movement. Such a strong slow-down corresponds to approximately 200-period simple moving average.

Formula of fractal dimension:

D = (LOG(N1 + N2) - LOG(N3))/LOG(2)
It is calculated based on the additional formula:

N(Length,i) = (HighestPrice(i) - LowestPrice(i))/Length
where:

HighestPrice(i) - current maximal value for Length periods;
LowestPrice(i) - current minimal value for Length periods;
Values N1, N2 and N3 are respectively equal to:

N1(i) = N(Length,i)
N2(i) = N(Length,i + Length)
N3(i) = N(2 * Length,i)

FRAMA(i) = A(i) * Price(i) + (1 - A(i)) * FRAMA(i-1)

where:

FRAMA(i) - current value of FRAMA;

Price(i) - current price;

FRAMA(i-1) - previous value of FRAMA;

A(i) - current factor of exponential smoothing.

Exponential smoothing factor is calculated according to the below formula:

A(i) = EXP(-4.6 * (D(i) - 1))

where:

D(i) - current fractal dimension;

EXP() - mathematical function of exponent.

Fractal dimension of a straight line is equal to one. It is seen from the formula that if D = 1, then A = EXP(-4.6 *(1-1)) = EXP(0) = 1. Thus if price changes in straight lines, exponential smoothing is not used, because in such a case the formula looks like this:

FRAMA(i) = 1 * Price(i) + (1 - i) * FRAMA(i-1) = Price(i)

I.e. the indicator exactly follows the price.

The fractal dimension of a plane is equal to two. From the formula we get that if D = 2, then the smoothing factor A = EXP(-4.6*(2-1)) = EXP(-4.6) = 0.01. Such a small value of the exponential smoothing factor is obtained at moments when price makes a strong saw-toothed movement. Such a strong slow-down corresponds to approximately 200-period simple moving average.

Formula of fractal dimension:

D = (LOG(N1 + N2) - LOG(N3))/LOG(2)

It is calculated based on the additional formula:

N(Length,i) = (HighestPrice(i) - LowestPrice(i))/Length

where:

HighestPrice(i) - current maximal value for Length periods;

LowestPrice(i) - current minimal value for Length periods;

Values N1, N2 and N3 are respectively equal to:

N1(i) = N(Length,i)

N2(i) = N(Length,i + Length)

N3(i) = N(2 * Length,i)

Is is possible to code these into PRT code (or incorporate this with your code) to compare the effectiveness of the FC and SC with the Log version?

Thanks,

Cheers
Brad

Bard

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12/06/2016 at 5:31 PM #17883

Nicolas

If you can find comprehensive formula from any other trading software (not from “R” like your first one), I could code the modified FRAMA for PRT of course.

Nicolas

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12/06/2016 at 10:18 PM #17907

Bard

Not from “R”?

Bard

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12/07/2016 at 11:59 AM #17922

Bard

Hi Nicholas,

You mean Copyrighted “C”?

This code has the fast and Slow Mov Averages and is logarithmic. Could you delete the other two codes above? Thanks (-:

study("Fractal Adaptive Moving Average",shorttitle="FRAMA",overlay=true)

price = close
len = input(defval=252,minval=1)
FC = input(defval=40,minval=1)
SC = input(defval=252,minval=1)

w = log(2/(SC+1))
len1 = len/2
H1 = highest(high,len1)
L1 = lowest(low,len1)
N1 = (H1 - L1)/len1

H2 = for i = len1+1 to len
    high>high[i]?high:high[i]
    
L2 = for i = len1+1 to len
    low>low[i]?low:low[i]

N2 = (H2 - L2)/len1

H3 = highest(high,len)
L3 = lowest(low,len)
N3 = (H1 - L1)/len

dimen = (log(H1+H2) - log(H3))/log(2)
oldalpha = exp(w*(dimen-1))
oldN = (2-oldalpha)/oldalpha
newN = ((SC-FC)*(oldN-1)/(SC-1))+FC
alpha = 2/(newN+1)
out = nz(out[1])*(1-alpha) + price*alpha

plot(out,title="FRAMA")

study("Fractal Adaptive Moving Average",shorttitle="FRAMA",overlay=true)

price = close

len = input(defval=252,minval=1)

FC = input(defval=40,minval=1)

SC = input(defval=252,minval=1)

w = log(2/(SC+1))

len1 = len/2

H1 = highest(high,len1)

L1 = lowest(low,len1)

N1 = (H1 - L1)/len1

H2 = for i = len1+1 to len

high>high[i]?high:high[i]

L2 = for i = len1+1 to len

low>low[i]?low:low[i]

N2 = (H2 - L2)/len1

H3 = highest(high,len)

L3 = lowest(low,len)

N3 = (H1 - L1)/len

dimen = (log(H1+H2) - log(H3))/log(2)

oldalpha = exp(w*(dimen-1))

oldN = (2-oldalpha)/oldalpha

newN = ((SC-FC)*(oldN-1)/(SC-1))+FC

alpha = 2/(newN+1)

out = nz(out[1])*(1-alpha) + price*alpha

plot(out,title="FRAMA")

Bard

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12/07/2016 at 3:26 PM #17936

Nicolas

Nope I meant “R”, the statistical analysis software: https://www.r-project.org/

This last new code is much more readable, I believe it can be converted to probuilder. Let me have a look.

Nicolas

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12/08/2016 at 10:05 AM #17985

Nicolas

Your last code proposal have some variables that aren’t used in the final calculation of the FRAMA. This prorealtime code is the result of the conversion, it returns a curve, I let you verify its information on your charts 🙂

price = close
len = 126 //FRAMA period
FC = 4 //fast constant--aka lowest n for an EMA
SC = 300 //slow constant--aka lowest n for an EMA

if barindex>len+fc+sc then
w = log(2/(SC+1))
len1 = len/2
H1 = highest[len1](high)
//L1 = lowest[len1](low)
//N1 = (H1 - L1)/len1

for i = len1+1 to len do
if high>high[i] then
H2 = high[i]
endif
next

//for i = len1+1 to len do
//if low>low[i] then
//L2  = low[i]
//endif
//next

//N2 = (H2 - L2)/len1

H3 = highest[len](high)
//L3 = lowest[len](low)
//N3 = (H1 - L1)/len

dimen = (log(H1+H2) - log(H3))/log(2)
oldalpha = exp(w*(dimen-1))
oldN = (2-oldalpha)/oldalpha
newN = ((SC-FC)*(oldN-1)/(SC-1))+FC
alpha = 2/(newN+1)
out = (out[1])*(1-alpha) + price*alpha
endif

RETURN out as "modified FRAMA"

price = close

len = 126 //FRAMA period

FC = 4 //fast constant--aka lowest n for an EMA

SC = 300 //slow constant--aka lowest n for an EMA

if barindex>len+fc+sc then

w = log(2/(SC+1))

len1 = len/2

H1 = highest[len1](high)

//L1 = lowest[len1](low)

//N1 = (H1 - L1)/len1

for i = len1+1 to len do

if high>high[i] then

H2 = high[i]

endif

//for i = len1+1 to len do

//if low>low[i] then

//L2 = low[i]

//endif

//next

//N2 = (H2 - L2)/len1

H3 = highest[len](high)

//L3 = lowest[len](low)

//N3 = (H1 - L1)/len

dimen = (log(H1+H2) - log(H3))/log(2)

oldalpha = exp(w*(dimen-1))

oldN = (2-oldalpha)/oldalpha

newN = ((SC-FC)*(oldN-1)/(SC-1))+FC

alpha = 2/(newN+1)

out = (out[1])*(1-alpha) + price*alpha

endif

RETURN out as "modified FRAMA"

Nicolas

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12/08/2016 at 12:40 PM #18057

supertiti

Avec FC = 40 SC = 250 LEN = 252 j’ai cela comme retour ?! la moyenne est “flat”

supertiti

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05/13/2017 at 11:27 PM #35462

laurenzo

Dans le code on a du

HH=High[len/2]
LL=Low[len/2]
 
For count=len/2 To len-1
If High[count] > HH Then
HH=High[count]
Endif

HH=High[len/2]

LL=Low[len/2]

For count=len/2 To len-1

If High[count] > HH Then

HH=High[count]

Endif

Tout va bien quand len est pair.

Si len est impaire, ça va planter on va essayer d’accéder à Low[décimal].

Du coup il faut faire un ROUND je suppose avant 🙂

genre High[ROUND(count)]

C’est pas super beau mais bon 🙂

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05/13/2017 at 11:51 PM #35463

laurenzo

Voilà mon code avec les rounds et le FIX sur le LOG

// FRAMA - Fractal Adaptive Moving Average by John Ehlers

// --- parameters
Series = CustomClose
// Period = 20
// ---

Period = MAX(Period, 1)

N3 = (highest[Period](High) - lowest[Period](Low)) / Period
mH = High
L = Low

FOR count = 0 TO (Period / 2) - 1 DO
    count = ROUND(count)
    IF High[count] > mH THEN
        mH = High[count]
    ENDIF
    IF Low[count] < L THEN
        L = Low[count]
    ENDIF
NEXT

N1 = (mH - L) / (Period / 2)
HH = High[ROUND(Period / 2)]
LL = Low[ROUND(Period / 2)]

FOR count = Period / 2 TO Period - 1 DO
    count = ROUND(count)
    IF High[count] > HH THEN
        HH = High[count]
    ENDIF
    IF Low[count] < LL THEN
        LL = Low[count]
    ENDIF
NEXT

N2 = (HH - LL) / (Period / 2)

IF N1 > 0 AND N2 > 0 AND N3 > 0 THEN
    // FIX LOG
    Dimen = ((LOG(N1 + N2) / LOG(10)) - (LOG(N3) / LOG(10))) / (LOG(2) / LOG(10))
ENDIF

alpha = EXP(-4.6 * (Dimen - 1))
IF alpha < 0.01 THEN
    alpha = 0.01
ELSIF alpha > 1 THEN
    alpha = 1
ENDIF

IF BarIndex < Period THEN
    FRAMA = Series
ELSE
    FRAMA = alpha * Series + (1 - alpha) * FRAMA[1]
ENDIF

RETURN FRAMA

// FRAMA - Fractal Adaptive Moving Average by John Ehlers

// --- parameters

Series = CustomClose

// Period = 20

// ---

Period = MAX(Period, 1)

N3 = (highest[Period](High) - lowest[Period](Low)) / Period

mH = High

L = Low

FOR count = 0 TO (Period / 2) - 1 DO

count = ROUND(count)

IF High[count] > mH THEN

mH = High[count]

ENDIF

IF Low[count] < L THEN

L = Low[count]

ENDIF

N1 = (mH - L) / (Period / 2)

HH = High[ROUND(Period / 2)]

LL = Low[ROUND(Period / 2)]

FOR count = Period / 2 TO Period - 1 DO

count = ROUND(count)

IF High[count] > HH THEN

HH = High[count]

ENDIF

IF Low[count] < LL THEN

LL = Low[count]

ENDIF

N2 = (HH - LL) / (Period / 2)

IF N1 > 0 AND N2 > 0 AND N3 > 0 THEN

// FIX LOG

Dimen = ((LOG(N1 + N2) / LOG(10)) - (LOG(N3) / LOG(10))) / (LOG(2) / LOG(10))

ENDIF

alpha = EXP(-4.6 * (Dimen - 1))

IF alpha < 0.01 THEN

alpha = 0.01

ELSIF alpha > 1 THEN

alpha = 1

ENDIF

IF BarIndex < Period THEN

FRAMA = Series

ELSE

FRAMA = alpha * Series + (1 - alpha) * FRAMA[1]

ENDIF

RETURN FRAMA

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05/14/2017 at 5:09 PM #35493

Bard

Appreciated, thanks @laurenzo.

Bard

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