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# Copyright 2006, 2007, 2009, 2010 Kevin Ryde |
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# This file is part of Chart. |
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# |
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# Chart is free software; you can redistribute it and/or modify it under the |
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# terms of the GNU General Public License as published by the Free Software |
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# Foundation; either version 3, or (at your option) any later version. |
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# |
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# Chart is distributed in the hope that it will be useful, but WITHOUT ANY |
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# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS |
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# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more |
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# details. |
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# |
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# You should have received a copy of the GNU General Public License along |
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# with Chart. If not, see <http://www.gnu.org/licenses/>. |
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package App::Chart::Series::Derived::DEMA; |
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use 5.010; |
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use strict; |
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use warnings; |
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use Carp; |
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use Locale::TextDomain 1.17; # for __p() |
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use Locale::TextDomain ('App-Chart'); |
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use base 'App::Chart::Series::Indicator'; |
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use App::Chart::Series::Derived::EMA; |
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use App::Chart::Series::Derived::EMAx2; |
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# http://www.stockworm.com/help/manual/double-ema.html |
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# Example graph PFE (what year?). |
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# |
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# http://trader.online.pl/ELZ/t-i-Double_Smoothed_Exponential_Moving_Average.html |
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# Tradestation example ^SPC 2001. |
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# |
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# http://store.traders.com/-v12-c01-smoothi-pdf.html |
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# Intro of TA S&C magazine, describing as faster. |
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# |
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# http://www.fmlabs.com/reference/DEMA.htm |
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# Formula only. |
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# |
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sub longname { __('DEMA - Double EMA') } |
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sub shortname { __('DEMA') } |
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sub manual { __p('manual-node','Double and Triple Exponential Moving Average') } |
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use constant |
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{ type => 'average', |
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priority => -10, |
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parameter_info => [ { name => __('Days'), |
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key => 'dema_days', |
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type => 'integer', |
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minimum => 0, |
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default => 20 } ], |
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}; |
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sub new { |
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my ($class, $parent, $N) = @_; |
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$N //= parameter_info()->[0]->{'default'}; |
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($N > 0) or croak "DEMA bad N: $N"; |
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return $class->SUPER::new |
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(parent => $parent, |
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parameters => [ $N ], |
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N => $N, |
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arrays => { values => [] }, |
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array_aliases => { }); |
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} |
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sub proc { |
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my ($class_or_self, $N) = @_; |
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my $ema_proc = App::Chart::Series::Derived::EMA->proc($N); |
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my $ema2_proc = App::Chart::Series::Derived::EMA->proc($N); |
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return sub { |
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my ($value) = @_; |
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my $e = $ema_proc->($value); |
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my $e2 = $ema2_proc->($e); |
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return 2*$e - $e2; |
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}; |
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} |
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# A DEMA is in theory influenced by all preceding data, but warmup_count() |
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# is designed to determine a warmup count. The next point will have an |
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# omitted weight of no more than 0.1% of the total. Omitting 0.1% should be |
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# negligable, unless past values are ridiculously bigger than recent ones. |
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# |
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# The implementation here does a binary search for the first i satisfying |
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# Omitted(i)<=0.001, so it's only moderately fast. |
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# |
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sub warmup_count { |
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my ($self_or_class, $N) = @_; |
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if ($N <= 1) { return 0; } |
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my $f = App::Chart::Series::Derived::EMA::N_to_f ($N); |
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return App::Chart::Series::Derived::EMAx2::bsearch_first_true |
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(sub { |
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my ($i) = @_; |
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return (dema_omitted($N,$f,$i) |
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<= App::Chart::Series::Derived::EMA::WARMUP_OMITTED_FRACTION) }, |
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$N); |
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} |
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# dema-omitted() returns the fraction (between 0 and 1) of absolute weight |
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# omitted by stopping a DEMA at the f^k term, which means the first k+1 |
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# terms. |
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# |
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# The EMA and EMAofEMA omitted totals are |
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# |
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# Q(k) = f^(k+1) |
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# R(k) = f^(k+1) * (k+2 - f * (k+1)) |
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# |
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# thus for the DEMA the net signed amount, implemented in |
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# dema_omitted_signed(), is |
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# |
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# S(k) = 2*Q(k) - R(k) |
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# = f^(k+1) * (f*(k+1) - k) |
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# |
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# This grows above 1 up to the f^N term, then the terms go negative and it |
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# decreases towards 1. |
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# |
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# The position of the negative/positive transition is always at f^N. The |
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# coefficient of that f^N term is |
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# |
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# 2 - (1-f)*(N+1) = 2 - (1-(N-1)/(N+1))*(N+1) |
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# = 2 - (N+1-(N-1)) |
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# = 2 - N - 1 + N - 1 |
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# = 0 |
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# |
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# An absolute omitted weight is calculated from the signed omitted amount. |
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# When k>N we can just negate the signed omitted. When k<N we add the |
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# negative terms past N in twice, first to cancel the negative then to add |
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# in as positive. |
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# |
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# The total of all the negatives beyond N is -S(N), |
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# |
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# tail = -S(N) = f^(N+1) * (f*(N+1) - N) |
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# = f^(N+1) * ((N-1)/(N+1) * (N+1) - N) |
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# = f^(N+1) * (N-1 - N) |
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# = f^(N+1) |
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# |
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# Thus the absolute omitted, |
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# |
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# T(k) = / - S(k) if k >= N |
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# \ S(k) + 2*f^(N+1) if k < N |
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# |
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# This is out of a total which is the positive and negative parts added as |
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# abolute values. Knowing pos+neg=1 and neg=-f^(N+1), |
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# |
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# total absolute weight = 1 + 2*f(N+1) |
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# |
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# And that total is applied as a divisor, so the return from `dema-omitted' |
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# is between 0 and 1. (It works to call it with k=-1 for no terms omitted, |
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# the result is 1.0.) |
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# |
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sub dema_omitted { |
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my ($N, $f, $k) = @_; |
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my $tail = $f ** ($N + 1); |
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my $num = dema_omitted_signed ($f, $k); |
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if ($k >= $N) { |
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$num = -$num; |
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} else { |
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$num += 2 * $tail; |
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} |
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return $num / (2*$tail + 1); |
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} |
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sub dema_omitted_signed { |
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my ($f, $k) = @_; |
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return $f**($k+1) * ($f*($k+1) - $k); |
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} |
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1; |
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__END__ |
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# =head1 NAME |
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# |
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# App::Chart::Series::Derived::DEMA -- double-exponential moving average |
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# |
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# =head1 SYNOPSIS |
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# |
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# my $series = $parent->DEMA($N); |
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# |
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# =head1 DESCRIPTION |
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# |
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# ... |
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# |
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# =head1 SEE ALSO |
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# |
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# L<App::Chart::Series>, L<App::Chart::Series::Derived::EMA> |
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# |
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# =cut |