# 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::RSquared;
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::Derived::SMA;
use constant DEBUG => 0;
# http://www.traderslog.com/r-squared.htm
# Sample Coors (NYSE symbol "TAP") from Feb 2002 (the year isn't shown,
# but is 2002).
#
# http://mathworld.wolfram.com/CorrelationCoefficient.html
# Explanation of general case, incl formulas.
#
sub longname { __('R-Squared Index') }
sub shortname { __('R-Squared') }
sub manual { __p('manual-node','R-Squared Index') }
use constant
{ type => 'indicator',
units => 'zero_to_one',
minimum => 0,
maximum => 1,
parameter_info => [ { name => __('Days'),
key => 'rsquared_days',
type => 'integer',
minimum => 1,
default => 14 } ],
};
sub new {
my ($class, $parent, $N) = @_;
$N //= parameter_info()->[0]->{'default'};
($N > 0) || croak "RSquared 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; # $N-1
# Return the factor for r-squared arising from the denominator Y variance.
# This is
#
# 1
# -------------------------------------------------
# n * (1^2 + 2^2 + ... + n^2) - (1 + 2 + ... + n)^2
#
# and the denominator here is (n^4 - n^2)/12, per the DEBUG code below.
#
sub yfactor {
my ($N) = @_;
if ($N < 2) { return 1; }
return 12.0 / ($N*$N * ($N*$N - 1));
}
if (DEBUG) {
my $triangle = sub {
my ($n) = @_;
return List::Util::sum (1 .. $n);
};
my $sum_squares = sub {
my ($n) = @_;
return List::Util::sum (map {$_**2} (1 .. $n));
};
my $yden = sub {
my ($n) = @_;
return $n * $sum_squares->($n) - ($triangle->($n))**2;
};
require Math::Polynomial;
require Math::BigRat;
Math::Polynomial->verbose(1);
Math::Polynomial->configure(VARIABLE => "\$N");
my $poly = Math::Polynomial::interpolate (map {
($_, Math::BigRat->new(12 * $yden->($_)))} (1..10));
say "yfactor 1/12 * ($poly)";
}
# return the triangular number of N, ie. N*(N+1)/2
sub triangular {
my ($n) = @_;
return $n * ($n+1) / 2;
}
sub proc {
my ($class, $N) = @_;
# This is the correlation coefficient of the last COUNT many X values,
# against a set of Y values 1, 2, 3, ..., COUNT. Or fewer than COUNT
# until that many values have been seen. The formula in the manual is
#
# (Covariance X,Y)^2
# r^2 = ---------------------------
# (Variance X) * (Variance Y)
#
# which is
#
# (Sum X*Y)/N - (Sum X)/N * (Sum Y)/N
# r^2 = -------------------------------------------------------------
# ((Sum X^2)/N - (Sum X)^2/N^2) * ((Sum Y^2)/N - (Sum Y)^2/N^2)
#
# But in the code a factor of N^2 is put through numerator and
# denominator to give
#
# N * Sum X*Y - Sum X * Sum Y
# r^2 = -----------------------------------------------------
# (N * Sum X^2 - (Sum X)^2) * (N * Sum Y^2 - (Sum Y)^2)
#
# In the degenerate case N==1, the variance of the Y values is 0, so
# r^2=0/0. Return 1 in that case, considering a single value is perfectly
# correlated.
#
# If all the X values are the same then r^2 = 0/0. Return 1 in that case,
# because those X values are a perfect straight line, a horizontal one.
#
#
# @array,$pos is a circular list of the last $N many X values.
#
# $count is the number of values in @array.
#
# $x_total is the sum of the values in @array.
#
# $xx_total is the sum of the squares of the values in @array.
#
# $y_total is the sum of the Y values corresponding to the values in
# @array, which means 1+2+...+$count, which is a triangular number. This
# varies until $count==$N is reached and is then a constant.
#
# $y_factor is the variance factor in the denominator, see yfactor()
# above. This varies until $count==$N is reached and is then a constant.
#
# $xy_total is the sum of the product x*y for each x,y pair, which means
# x[1]*1 + x[2]*2 + ... + x[POINTS]*POINTS. When shifting out an old X,
# the weighting of each x in the sum is reduced by subtracting X-TOTAL.
#
my @array;
my $pos = $N - 1; # initial extends
my $x_total = 0;
my $xx_total = 0;
my $y_total = 0;
my $y_factor = 0;
my $xy_total = 0;
my $count = 0;
return sub {
my ($x) = @_;
if ($count >= $N) {
# drop oldest point
my $prev_x = $array[$pos];
$xy_total -= $x_total;
$x_total -= $prev_x;
$xx_total -= $prev_x ** 2;
} else {
# gaining a point
$count++;
$y_factor = yfactor($count);
$y_total = triangular($count);
}
$array[$pos] = $x;
if (++$pos >= $N) { $pos = 0; }
# add this point
$x_total += $x;
$xx_total += $x*$x;
$xy_total += $x * $count;
my $den = $xx_total*$count - $x_total*$x_total;
if ($den == 0) { return 1; }
return $y_factor * ($xy_total*$count - $x_total*$y_total)**2 / $den;
};
}
1;
__END__
# =head1 NAME
#
# App::Chart::Series::Derived::RSquared -- R squared index
#
# =head1 SYNOPSIS
#
# my $series = $parent->RSquared($N);
#
# =head1 DESCRIPTION
#
# ...
#
# =head1 SEE ALSO
#
# L<App::Chart::Series>
#
# =cut