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lib/App/Chart/Series/Derived/LinRegStderr.pm  view on Meta::CPAN

#     without calculating a,b parameters.
#
#
#
#               Sum (y - (a+b*x))^2
# stderr = sqrt -------------------
#                       N^2
#
#               Sum ((y - My) - b*x)^2
#        = sqrt ----------------------     where My = Mean(Y)
#                       N^2
#
#               Sum (y - My)^2 - 2*My*b*x + b^2*x^2
#        = sqrt -----------------------------------
#                               N^2
#
#                   (y - My)^2       2*My*b*x - b^2*x^2
#        = sqrt Sum ---------- - Sum ------------------
#                    N^2                    N^2
#
# The first term is Variance(Y), and with b = Mean(X*Y) - Mean(X) * Mean(Y)
#
#                            2*M(y)*Sum(x) - M(X*Y)*Sum(x^2)/M(X)*M(Y)
#        = sqrt Var(Y) - b * -----------------------------------------
#                                               N^2
#
# ....


sub longname  { __('Linear Regression Stderr') }
sub shortname { __('Linreg Stderr') }
sub manual    { __p('manual-node','Linear Regression Standard Error') }

use constant
  { type       => 'indicator',
    units      => 'price',
    priority   => -10,
    minimum    => 0,
    parameter_info => [ { name    => __('Days'),
                          key     => 'linregstderr_days',
                          type    => 'integer',
                          minimum => 1,
                          default => 20 } ],
  };

sub new {
  my ($class, $parent, $N) = @_;

  $N //= parameter_info()->[0]->{'default'};
  ($N > 0) || croak "LinRegStderr 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 1/Variance(X) arising in the stderr formula.  With
# X values -1.5,-0.5,0.5, 1.5 this means
#
#                         1
#      --------------------------------------------
#      n * ((-1.5)^2 + (-0.5)^2 + (0.5)^2 + (1.5)^2)
#
# and the denominator here is (n^4 - n^2)/12.  See devel/ema-omitted.pl for
# checking this.  Same func in RSquared.pm too.
#
sub xfactor {
  my ($N) = @_;
  if ($N < 2) { return 1; }
  return 12.0 / ($N*$N * ($N*$N - 1));
}

sub proc {
  my ($class, $N) = @_;

  # @array,$pos is a  circular list of the last $N many Y values.
  #
  # $count is the number of values in @array.
  #
  # $y_total is the sum of the values in @array.
  #
  # $yy_total is the sum of the squares of the values in @array.
  #
  # $x_total is the sum of the X values corresponding to the values in
  # @array, which means 1+2+...+$count, which is a triangular number.  This
  # varies until $count==$N is reached, and is then a constant.
  #
  # $x_factor is the variance factor in the denominator, see `xfactor' 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
  # 1*y[1] + 2*y[2] + ... + $count*y[$count].  When shifting out an old Y,
  # the weighting of each y in the sum is reduced by subtracting $y_total.

  my @array;
  my $pos = $N - 1;  # initial extends
  my $y_total = 0;
  my $yy_total = 0;
  my $x_factor = 0;
  my $xy_total = 0;

  my $count = 0;
  return sub {
    my ($y) = @_;

    if ($count >= $N) {
      # drop oldest point
      my $prev = $array[$pos];
      $yy_total -= $prev ** 2;
      $xy_total += ($count-1)*0.5 * $prev;
      $y_total -= $prev;
    } else {
      # gaining a point
      $count++;
      $x_factor = xfactor($count);
      $xy_total += $y_total * 0.5; # adj so 0.5 less each x
    }