If performance matters then temporaries may be your friend. For instance the following should run several times faster than your code:

foreach my $month ('02'..'03') {
  my $m_bucket = $bucket{$month} = {};
  foreach my $day ('00' .. $mons{$month}) {
    my $d_bucket = $m_bucket->{$day} = {};
    foreach my $hour ('00'..'23') {
      my $h_bucket = $d_bucket->{$hour} = {};
      foreach my $minute ('00'..'59') {
        $h_bucket->{$minute} = [0,0];
      }
    }
  }
}
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(A useful trick I have put to good use in the past.)