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Trying to Calculate AMA

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im trying to calculate the AMA but iam not quite sure if i understand the calculation correctly yet. Till now i have calculated SMA, WMA and EMA and wanted to have the AMA too because i think its nice to find out if the market is doing a rallye, crash or is simply movind sidewards..


I tried to understand the calculation from here: http://user42.tuxfamily.org/chart/manual/Kaufman-Adaptive-Moving-Average.html#Kaufman-Adaptive-Moving-Average


Besides... the JMA was praised here in the forum as the best AMA... while on another site i found that its only calculated over a shorter period of time and therefore its more near at the actual price. Is that correct? So is the JMA only a AMA with less previous prices taken into account so that a smaller AMA will show the same results than the JMA?


Anyway... i understand it so that when calculating an EMA for 10 days closing price i would create a AMA for these 10 days too.


          abs (close[today] - close[N days ago])
    ER = --------------------------------------
             Sum     abs (close - close[prev])
          past N days


So first you have to create the Efficiency ratio. Its the closing price of today minus the closing price before N days, in this case 10. Then take abs from the result which means cutting a possibly negative minus.

Then divide this through the sum of all past 10 days closing prices including the actual one. Multiplied(?) with the abs of actual closeprice minus closeprice of day before.

Then you have the ER.


Then calculate alpha with the calculated ER:

alpha = (ER * 0.6015 + 0.0645) ^ 2


But i dont see where these numbers are from. Are they hardcoded?


The next step is to calc:


KAMA = alpha * close + (1-alpha) * KAMA[prev]


Which means you need the actual closeprice again and the previous KAMA. If you dont have a previous kama do you use simply the SMA or the mentioned EMA for the actual day and start the next day calculating the KAMA? Similar you do it for an EMA?


You see im not quite sure how its calculated. The other MA had better and more explainations. Though they were easier to understand too.


Someone can help me here?



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my suggestion is to stay with SMA or XMA.


if you don't understand the complications,

it is most likely going to bite you when you are least expected.


after all, ma is ma... KISS.

The further you are removed from the raw price,

the further you are from reality.

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Thanks for your suggestion. But i only want to use the AMA for identifying the kind of direction a price is taking. Its not that i want to use it to specify the price to buy or sell from that. Only to change the trading strategy.


But yesterday i found a website that contained a .xls file: Forums - Jurik indicator for Excel


I didnt look too far in it but it looks like i shouldnt have trouble creating my own AMA with it. I couldnt mention that yesterday because the admins didnt have put my thread to visible at that point.



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here is the T3 function - maybe somekind usefull adaptive smoothing ...........

call T3Average(value1,Length) in an indicator


{ *******************************************************************


Function : T3Average


Last Edit : 12/14/97 - 05/01/99


Provided By : Bob Fulks

Recoded By: : Clyde Lee for speed and really simple function


Description : This function is an EasyLanguage version of the

moving average described in the January. 1998 issue of TASC,

p57, "Smoothing Techniques for More Accurate Signals", by Tim

Tillson. It is translated from the MetaStock code presented

in the article. The function was modified by C. Lee to not use

any call to external exponential average function but rather

perform the same operation internally. This saves the

overhead of a bunch of calls to the XAverage function. This

modification increases speed and allows variables as inputs.


The variable, "b", is a damping coefficient which is set to

the suggested default value of 0.7. The variable "b" is

substituted for the variable, "a" used in the article since

"a" is a reserved word.


The resulting indicator plotting this function appears to

duplicate the results shown in Figure 4 of the article.


Damp: A damping factor = any value between +100 and -100:


-100 = No damping (with ringing)

0 = Critically damped for a triangle wave.

+100 = Overdamped


Lag: The lag in bars is given by:


Lag = (Length - 1) * (1 + Damp / 100) / 2


The Lag is equal to the lag of an exponential or simple

moving average of the same "Length" when Damp = 0. When

Damp = -100 then Lag = 0 but there is ringing and overshoot

as with a linear regression value.


© 2000 Bob Fulks, All rights reserved.

only portion dealing with damp ! ! !



Inputs: Price(NumericSimple), Period(NumericSimple);

Variables: e1(Price), e2(Price), e3(Price),

e4(Price), e5(Price), e6(Price);

Variables: XAlpha(2/6), XBeta(0), OldPeriod(-999999);

Vars: damp(-70),

b(-0.01 * damp),

aa(b*b), aaa(b*b*b),

c1(-aaa), c2(3*aa+3*aaa),

c3(-6*aa-3*b-3*aaa), c4(1+3*b+aaa+3*aa);


If Period<>0 then begin

If Period<>OldPeriod then begin;






e1 = e1*XBeta + Price*Xalpha;

e2 = e2*XBeta + e1 *Xalpha;

e3 = e3*XBeta + e2 *Xalpha;

e4 = e4*XBeta + e3 *Xalpha;

e5 = e5*XBeta + e4 *Xalpha;

e6 = e6*XBeta + e5 *Xalpha;



T3Average = c1*e6 + c2*e5 + c3*e4 + c4*e3;


Else T3Average=Price;


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Here is some hard easy language that may make it easier for you to find answers to your questions. hth


[LegacyColorValue = true]; 

{ Kaufman's Adaptive Moving Average }

Price( numericseries ), 
EffRatioLength( numericsimple ), 
FastAvgLength( numericsimple ), { this input assumed to be a constant >= 1 }
SlowAvgLength( numericsimple ) ; { this input assumed to be a constant >= 1 }

{ Eff = Efficiency }

NetChg( 0 ), 
TotChg( 0 ), 
EffRatio( 0 ), 
ScaledSFSqr( 0 ), 
SlowAvgSF( 2 / ( SlowAvgLength + 1 ) ), 
FastAvgSF( 2 / ( FastAvgLength + 1 ) ), 
SFDiff( FastAvgSF - SlowAvgSF ) ;

{ Eff = Efficiency, SF = Smoothing Factor }

if CurrentBar = 1 then
fKaufmanAMA = Price
NetChg = AbsValue( Price - Price[ EffRatioLength ] ) ;
TotChg = Summation( AbsValue( Price - Price[1] ), EffRatioLength ) ;
if TotChg > 0 then
	EffRatio = NetChg / TotChg 
	EffRatio = 0 ;
{ note that EffRatio is somewhat similar to RSI }
ScaledSFSqr = Square( SlowAvgSF + EffRatio * SFDiff ) ;
fKaufmanAMA = fKaufmanAMA[1] + ScaledSFSqr * ( Price - fKaufmanAMA[1] ) ;
end ;

{ ** Copyright (c) 1991-2003 TradeStation Technologies, Inc. All rights reserved. ** 
 ** TradeStation reserves the right to modify or overwrite this analysis technique 
    with each release

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If you'd like a PDF of the original Kaufman paper describing this indicator and its applications, let me know. However, I personally would recommend heeding the advice given by Tams. Keep in mid also that the AMA is an 'old' solution to the problems it addresses, and far more mathematically advanced approaches have subsequently emerged from the fields of signal processing and time series analysis.



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I managed to create a working version in php now. I tested it with several sets of data and the results matched so im sure i worked correctly.


Heres my function in php:

  function bc_kama($average_array, $price_type, $tstf_id, $tsset_id, $tsp_id) {
   global $db;
   $actual_price = $average_array[count($average_array) - 1][$price_type];
   $last_kama = $this->ask_db('trades_stat_average_stats', 'tsset_id_ref = \''. $tsset_id .'\' and tsp_id_ref < \''. $tsp_id .'\'', 'price', 'tsp_id_ref desc', '1');
   if(!isset($last_kama)) return $actual_price;
   $res = '0';
   for($x = 1; $x < count($average_array); $x++) {
     $res = bcadd($res, str_abs(bcsub($average_array[$x][$price_type], $average_array[$x - 1][$price_type])));
   $price_before_average_range_res = $this->ask_db('trades_stat_prices', 'tstf_id_ref = \''. $tstf_id .'\' and tsp_id_ref < \''. $tsp_id .'\'', 'price', 'tsp_id_ref desc', strval(count($average_array)));
   while($row = $db->fetch_array($price_before_average_range_res)){
     $price_before_average_range = $row['price'];
   $res = bcadd($res, str_abs(bcsub($average_array[0][$price_type], $price_before_average_range)));
   return bcadd($last_kama, bcmul(bcpow(bcadd(bcmul(bcdiv(str_abs(bcsub($actual_price, $price_before_average_range)), $res), bcsub('0.6667', '0.0645')), '0.0645'), '2'), bcsub($actual_price, $last_kama)), MONEY_DECIMAL_PLACES);


The parameters are: average_array contains a set of the previous prices. Its so many entries long how the range for the average should be.

$price_type is a string giving the type of price for a timeframe because i use more than close price for calculations. For example high or low price too.

The rest are only for database-requests i have to do.


First line gives the actual price of that day/timeframe.

Then get the last KAMA-Value from previous timeframe.

If there is not previous KAMA then return the actual (close) price. Thats how kama starts. not like with EMA where you start the first time with SMA-Value.

If there is a previous KAMA then move on by calculating the real kama.

Unfortunately the KAMA needs more than the amount of data the average should be. One entry more. Thats $price_before_average_range_res is needed.


Its not the best coding but it works and maybe someone the code helps someone.


What MAs are a better solution? I have read here that JMA is better but found on another site that its only a KAMA with less timeframes taken into account.

So what MAs are worth to look into?

I find the website etfhq.com interesting too because of their tests for MAs. They tested the performance of MAs against each other to find out who is performing better for trading.


The result in my eyes is that the simple and mostly older MAs have an advantage mostly.




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