I tried to redirect the output of the time command, but I couldn\'t:
$time ls > filename
real 0m0.000s
user 0m0.000s
sys 0m0.000s
The command time sends it's output to STDERR (instead of STDOUT). That's because the command executed with time normally (in this case ls) outputs to STDOUT.
If you want to capture the output of time, then type:
(time ls) 2> filename
That captures only the output of time, but the output of ls goes normal to the console. If you want to capture both in one file, type:
(time ls) &> filename
2> redirects STDERR, &> redirects both.