| Subject: | Laguerre Moving Average |
Did some more work on finding a better moving average and came upon the
laguerre polynomial filter. Looks like the best so far. Very smooth
and responsive. You can find more info at:
http://www.mesasoftware.com/technicalpapers.htm - look for the Time Warp
paper.
Hacked out some POS code based on the paper, don't laugh, maybe you can
make a module out of it. Email me if it's too confusing.
Thanks,
John Baker
| Subject: | laguerre.filter.pl |
#!/usr/bin/perl
use List::Util qw(max min);
sub Median { # median may or may not be an element of the array
# got this from Math::NumberCruncher
my $arrayref = shift;
return undef unless defined $arrayref && @$arrayref > 0;
my @array = sort { $a <=> $b } @$arrayref;
if ( @array % 2 ) {
$median = $array[ @array / 2 ];
}
else {
$median = ( $array[ @array / 2 - 1 ] + $array[ @array / 2 ] ) / 2;
}
return $median;
}
sub FIR {
my $price1 = $_[0];
my $price2 = $_[1];
my $price3 = $_[2];
my $price4 = $_[3];
return ( ( $price1 + 2 * $price2 + 2 * $price3 + $price4 ) / 6 );
}
sub dollar_round {
my $n = shift;
my $minus = $n < 0 ? '-' : '';
$n = abs($n);
$n = int( ( $n + .005 ) * 100 ) / 100;
$n .= '.00' unless $n =~ /\./;
$n .= '0' if substr( $n, ( length($n) - 2 ), 1 ) == '.';
chop $n if $n =~ /\.\d\d0$/;
return "$minus$n";
}
my $L0;
my $L1;
my $L2;
my $L3;
my $gamma = .8; #Starting Gamma, will change
my $length = 20; #Set Days for gamma adjustment
my $counter;
# used last 50 odd days of IWM for testdata
@testdata = qw (
70.92 71.67 71.68 70.37 70.55 71.23 71.90 72.38 71.74 71.40
72.63 72.55 72.27 72.86 71.56 71.71 71.50 73.07 73.49 73.40
73.55 73.95 73.97 73.70 72.65 73.17 72.21 73.32 73.66 74.41
74.67 73.99 73.84 74.30 76.20 73.92 73.68 73.14 71.87 72.02
73.32 73.78 73.72 73.13 73.74 72.57 71.89 70.70 71.50 69.66
69.73 69.05);
$L0 = $L1 = $L2 = $L3 = $testdata[0];
foreach $datum (@testdata) {
# gcf array holds the variances between the latest price and the last
# filter value
push @gcf, abs( $datum - $firfilter[ $counter - 1 ] ) if $counter > 0;
shift @gcf
if $counter >= $length; # we only want to see the last $length values
$L0A = $L0;
$L1A = $L1;
$L2A = $L2;
$L3A = $L3;
$L0 = $gamma * $datum + ( 1 - $gamma ) * $L0A;
$L1 = -( 1 - $gamma ) * $L0 + $L0A + ( 1 - $gamma ) * $L1A;
$L2 = -( 1 - $gamma ) * $L1 + $L1A + ( 1 - $gamma ) * $L2A;
$L3 = -( 1 - $gamma ) * $L2 + $L2A + ( 1 - $gamma ) * $L3A;
push @firfilter, FIR( $L0, $L1, $L2, $L3 );
$counter++;
if ( $counter >= $length ) { # we have enough values
my $highesthigh = max(@gcf); # the greatest variance
my $lowestlow = min(@gcf); # the least variance
my @lastfive = @gcf; # splice off the last five of this below
my @gammafinder;
# calculates the gamma as per the paper; the author recommended
# the last five bars
for ( splice( @lastfive, $#lastfive - 4 ) ) {
if ( $highesthigh - $lowestlow != 0 ) {
push @gammafinder,
( $_ - $lowestlow ) / ( $highesthigh - $lowestlow );
}
}
# voila, adjustable gamma
$gamma = Median( \@gammafinder );
print dollar_round($gamma), "\t",
dollar_round( $firfilter[ $counter - 1 ] ), "\n";
}
}