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Author image Torsten Förtsch

NAME

Math::EMA - compute the exponential moving average

SYNOPSIS

  use Math::EMA;
  my $avg=Math::EMA->new(alpha=>0.926119, ema=>$initial_value);
  $avg->set_param($iterations, $end_weight);
  $avg->alpha=$new_alpha;
  $avg->ema=$new_value;
  $avg->add($some_value);
  my $ema=$avg->ema;

DESCRIPTION

This module computes an exponential moving average by the following formula

  avg(n+1) = (1 - alpha) * new_value + alpha * avg(n)

where alpha is a number between 0 and 1.

That means a new value influences the average with a certain weight (1-alpha). That weight then exponentially vanes when other values are added.

How to choose alpha?

The value of alpha determines how fast a given value vanes but it never completely drops out. Assume you can define a limit say after 10 iterations the weight of a certain value should be 1% or 0.01. Then

               _____
         _10  /     `
 alpha =  \  / 0.01   = exp( log(0.01) / 10 )
           \/

Methods

Math::EMA->new( key=>value, ... )

creates a new Math::EMA object. Parameters are passed as key=>value pairs. Currently these keys are recognized:

  • alpha

    initializes alpha. Alpha must be in the range from 0 to 1.

  • ema

    initializes the average. If an uninitialized ema is used the first value being added initializes it.

$obj->alpha

set or retrieve the current alpha

$obj->ema

set or retrieve the current average

$obj->set_param($iterations, $end_weight)

computes alpha from the passed values. After $iterations new values a certain value should have a weight of $end_weight in the average.

SEE ALSO

http://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average

http://en.wikipedia.org/wiki/Exponential_smoothing#The_exponential_moving_average

AUTHOR

Torsten Förtsch, <torsten.foertsch@gmx.net>

COPYRIGHT AND LICENSE

Copyright (C) 2008 by Torsten Foertsch

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.10.0 or, at your option, any later version of Perl 5 you may have available.