# Copyright 2006, 2007, 2009, 2010 Kevin Ryde # This file is part of Chart. # # Chart is free software; you can redistribute it and/or modify it under the # terms of the GNU General Public License as published by the Free Software # Foundation; either version 3, or (at your option) any later version. # # Chart is distributed in the hope that it will be useful, but WITHOUT ANY # WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS # FOR A PARTICULAR PURPOSE. See the GNU General Public License for more # details. # # You should have received a copy of the GNU General Public License along # with Chart. If not, see . package App::Chart::Series::Derived::ZLEMA; use 5.010; use strict; use warnings; use Carp; use Locale::TextDomain 1.17; # for __p() use Locale::TextDomain ('App-Chart'); use base 'App::Chart::Series::Indicator'; use App::Chart::Series::Calculation; use App::Chart::Series::Derived::EMA; # http://www.linnsoft.com/tour/techind/movAvg.htm # Showing as EMA of "2*price-price[lag]", where lag=(n-1)/2 # # http://www.mesasoftware.com/technicalpapers.htm # http://www.mesasoftware.com/Papers/ZERO%20LAG.pdf # John Ehlers on zero lag, with graphs of frequency response. # sub longname { __('ZLEMA - Zero Lag EMA') } sub shortname { __('ZLEMA') } sub manual { __p('manual-node','Zero-Lag Exponential Moving Average') } use constant { type => 'average', parameter_info => [ { name => __('Days'), key => 'zlema_days', type => 'integer', minimum => 0, default => 20 } ], }; sub new { my ($class, $parent, $N) = @_; $N //= parameter_info()->[0]->{'default'}; ($N > 0) or croak "ZLEMA bad N: $N"; return $class->SUPER::new (parent => $parent, parameters => [ $N ], N => $N, lag => int (($N - 1) / 2), # (N-1)/2 arrays => { values => [] }, array_aliases => { }); } # Lag calculation: # # Taking a decreasing sequence with today price 0, yesterday price 1, the # day before 2, etc, then the EMA today using the power formula is # # EMA = (1-f) * (0 + 1*f + 2*f^2 + 3*f^3 + 4*f^4 + ...) # # Multiplying through gives # # EMA = 0 + 1*f + 2*f^2 + 3*f^3 + 4*f^4 + ... # - 0*f - 1*f^2 - 2*f^2 - 3*f^4 - ... # # = f + f^2 + f^3 + f^4 + ... # # = f * 1/(1-f) # # And with f=1-2/(N+1) meaning 1-f=2/(N+1), and also f=(N-1)/(N+1), # # N-1 N+1 # EMA = --- * --- # N+1 2 # # So EMA = (N-1)/2. Ie. the EMA is the value as at (N-1)/2 days ago, which # is the lag. # sub N_to_lag { my ($N) = @_; return int (($N - 1) / 2); } # A ZLEMA is in theory influenced by all preceding data, but warmup_count() # is designed to determine a warmup count. The next point will have an # omitted weight of no more than 0.1% of the total. Omitting 0.1% should be # negligable, unless past values are ridiculously bigger than recent ones. # # ENHANCE-ME: This is almost certainly an over-estimate since some of the # EMA and its prev terms cancel out. # sub warmup_count { my ($self_or_class, $N) = @_; return N_to_lag($N) + App::Chart::Series::Derived::EMA->warmup_count($N); } sub proc { my ($class_or_self, $N) = @_; my $lag = N_to_lag ($N); my $delay_proc = App::Chart::Series::Calculation->delay ($lag); my $ema_proc = App::Chart::Series::Derived::EMA->proc ($N); # FIXME: should still be able to follow weights when no $prev yet return sub { my ($value) = @_; my $ema = $ema_proc->($value); my $prev = $delay_proc->($ema) // $ema; return 2*$ema - $prev; }; } 1; __END__ # =head1 NAME # # App::Chart::Series::Derived::ZLEMA -- zero-lag exponential moving average # # =head1 SYNOPSIS # # my $series = $parent->ZLEMA($N); # # =head1 DESCRIPTION # # ... # # =head1 SEE ALSO # # L, L # # =cut