$raw_dataPtr = \%{$element_stats_hash{$element_name}{'raw_data'}};
$$raw_dataPtr{$time} = {$var};
[download]

I think you want something like this:

#!/usr/bin/perl

use Data::Dumper;

my $time = time();
my $val  = 0.12205589;
my $element_name = "foo";

$element_stats_hash{$element_name}{'raw_data'}{$time} = $val;   # <--

print Dumper $element_stats_hash{$element_name};

__END__
$VAR1 = {
          'raw_data' => {
                          '1229382894' => '0.12205589'
                        }
        };
[download]

Update: That said, there's nothing wrong with using an intermediate variable, in particular if you should end up needing it multiple times:

# init raw data hash somewhere
$element_stats_hash{$element_name}{'raw_data'} = {};

# then later
my $raw_data = $element_stats_hash{$element_name}{'raw_data'};
$raw_data->{$time} = $val;
$raw_data->{$another_time} = $another_val;
#...
[download]

But note the difference with respect to autovivication... which is why we need to init an (empty) 'raw data' hash in this case, before we can take a ref to it.

Also, please use the arrow syntax for dereferencing — it's much more readable (and less ambiguous) than $$raw_data{$time} when the expressions get more complex...