The Time::Local core module, along with localtime, can get you day, month and year periods pretty easily:

#!/usr/bin/perl
use strict;
use warnings;

use Time::Local;

my $t = time;    ## or, plug in your own timestamp

my ($day_start,   $day_end)   = day_period   ($t);
my ($month_start, $month_end) = month_period ($t);
my ($year_start,  $year_end)  = year_period  ($t);

print "The day starts at ", scalar localtime $day_start, "\n";
print "The day ends at ",   scalar localtime $day_end,   "\n";

print "The month starts at ", scalar localtime $month_start, "\n";
print "The month ends at ",   scalar localtime $month_end,   "\n";

print "The year starts at ", scalar localtime $year_start, "\n";
print "The year ends at ",   scalar localtime $year_end,   "\n";


sub day_period {
    my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localti
+me shift;
    my $t1 = timelocal (0, 0, 0, $mday,   $mon, $year);
    my $t2 = timelocal (0, 0, 0, $mday+1, $mon, $year);
    wantarray ? ($t1, $t2) : \($t1, $t2)
}

sub month_period {
    my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localti
+me shift;
    my $t1 = timelocal (0, 0, 0, 1, $mon,   $year);
    my $t2 = timelocal (0, 0, 0, 1, $mon+1, $year);
    wantarray ? ($t1, $t2) : \($t1, $t2)
}

sub year_period {
    my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localti
+me shift;
    my $t1 = timelocal (0, 0, 0, 1, 0, $year  );
    my $t2 = timelocal (0, 0, 0, 1, 0, $year+1);
    wantarray ? ($t1, $t2) : \($t1, $t2)
}
[download]

Output:

The day starts at Sat Nov  3 00:00:00 2007
The day ends at Sun Nov  4 00:00:00 2007
The month starts at Thu Nov  1 00:00:00 2007
The month ends at Sat Dec  1 00:00:00 2007
The year starts at Mon Jan  1 00:00:00 2007
The year ends at Tue Jan  1 00:00:00 2008
[download]

If you need week-long periods, you can either use a heavier, non-core module like Date::Manip, or write the logic yourself (hope you like special cases!).

Update: And if you want the periods to end just at the end of the day/month/year rather than at the beginning of the next one... subtract 1 from $XXXX_end.