# Copyright 2007, 2009, 2010, 2011 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 <http://www.gnu.org/licenses/>.
package App::Chart::Series::Derived::EPMA;
use 5.010;
use strict;
use warnings;
use Carp;
use List::Util qw(min max);
use Locale::TextDomain ('App-Chart');
use base 'App::Chart::Series::Indicator';
use App::Chart::Series::Calculation;
use App::Chart::Series::Derived::SMA;
# As EPMA:
#
# http://www.linnsoft.com/tour/techind/movAvg.htm
# Formulas LSMA as endpoint, and EPMA as weightings "3*i-n-1".
# Sample Nasdaq 100 (symbol QQQ, yahoo now ^IXIC) from 2001 of both
# (they come out the same).
#
# http://www.traders.com/Documentation/FEEDbk_docs/Archive/062001/Letters/Letters.html
# TASC letters June 2001, Don Kraska on the equivalence of his "3j-m-1"
# (j=1 to j=m where price[m] latest), with what John Bellantoni
# described in April 2001 letters.
#
# http://www.traders.com/Documentation/FEEDbk_docs/Archive/0198/Abstracts_new/TILLSON/Tillson9801.html
# Excerpt from TASC January 1998. Sample chart of EPMA (and IE/2) on
# Hewlett Packard (symbol HPQ) from 1996/7.
#
#
# As LSQMA:
#
# http://www.fmlabs.com/reference/LstSqrMA.htm
# Formula, described as LSQMA.
#
#
# Time Series Forecast:
#
# http://www.marketscreen.com/help/AtoZ/default.asp?hideHF=&Num=102
# Sample chart of microsoft (symbol MSFT) from 1992, split adjusted.
#
# http://www.prophet.net/analyze/popglossary.jsp?studyid=TSF
# http://www.traderslog.com/time-series-forecast.htm (same chart)
# Sample chart of fisher scientific .. but what symbol, what year?
#
#
# As "Modified Moving Average":
#
# http://www.traders.com/Documentation/FEEDbk_docs/Archive/012000/Abstracts_new/Sharp/Sharp.html
# Start of Joe Sharp's TASC article January 2000 (rest for sale).
#
# http://www.traders.com/Documentation/FEEDbk_docs/Archive/012000/TradersTips/TradersTips.html
# TASC traders' tips January 2000, various formulas.
# Technifilter coefficients look doubtful.
#
# http://www.traders.com/Documentation/FEEDbk_docs/Archive/062000/Letters/Letters.html
# TASC letters June 2000, Tim O'Sullivan pointing out MMA is the same
# as EPMA.
#
# http://www.linnsoft.com/tour/techind/mma.htm
# Formula, but sample chart is only an intraday.
#
# http://trader.online.pl/MSZ/e-w-Modified_Moving_Average.html
# Formulas for N=2, N=3, N=4, and N=10.
# http://trader.online.pl/MSZ/e-w-Modified_Moving_Average_II.html
# Formulas for N=20.
# http://trader.online.pl/ELZ/t-i-Modified_Moving_Averages.html
# Formula for general N, per traders tips, from www.omegaresearch.com.
# Sample chart S&P 500 (yahoo symbol ^GSPC) from 2001, looks like the
# default N=2 shown in the formula.
#
# http://www.tradecision.com/support/tasc_tips/modified_moving_average.htm
# http://www.tradecision.com/downloads/tasc_tips/ModifiedMovingAverage.tnd
# Formula.
#
#-----------------------------------------------------------------------------
# The equivalence of the linreg a+b*endpos and the "3i" stepping weighted
# moving average is easily shown. With a=mean, b=slope, p0 today, p1
# yesterday, etc, then a+b*endpos is
#
# p0 + p1 + ... + pN (N-1) (N-1)/2 * p0 + ... + (-(N-1)/2) * pN
# ------------------ + ----- * ----------------------------------
# N 2 ((N-1)/2)^2 + ... + (-(N-1)/2)^2
#
# The sum of the squares in the denominator is (N^3-N)/12 which is
# N*(N+1)*(N-1)/12 so the N-1 factor cancels, leaving a factor on each p[i]
#
# 1 1 12 * ((N-1)/2 - i)
# --- + --- * -------------------
# N 2 N*(N+1)
#
# which is
#
# N+1 + 3N - 3 - 6i
# -----------------
# N*(N+1)
#
# and then
#
# 2N - 1 - 3i
# ----------
# N*(N+1)/2
#
# Weights like that can be used directly to calculate the EPMA, but for now
# let the linreg-calc-proc code do the work.
sub longname { __('EPMA - Endpoint MA') }
sub shortname { __('EPMA') }
sub manual { __p('manual-node','Endpoint Moving Average') }
use constant
{ type => 'average',
units => 'price-slope',
parameter_info => [ { name => __('Days'),
key => 'epma_days',
type => 'integer',
minimum => 1,
default => 20 } ],
};
sub new {
my ($class, $parent, $N) = @_;
$N //= parameter_info()->[0]->{'default'};
($N > 0) || croak "EPMA bad N: $N";
return $class->SUPER::new
(parent => $parent,
N => $N,
parameters => [ $N ],
arrays => { values => [] },
array_aliases => { });
}
*warmup_count = \&App::Chart::Series::Derived::SMA::warmup_count; # $N-1
sub proc {
my ($class, $N) = @_;
my $linreg_proc = App::Chart::Series::Calculation->linreg($N);
return sub {
my ($y) = @_;
return ($linreg_proc->($y))[0];
};
}
1;
__END__
# =head1 NAME
#
# App::Chart::Series::Derived::EPMA -- endpoint moving average
#
# =head1 SYNOPSIS
#
# my $series = $parent->EPMA($N);
#
# =head1 DESCRIPTION
#
# ...
#
# =head1 SEE ALSO
#
# L<App::Chart::Series>
#
# =cut