You could use
f = find ( y > threshold )
to find the indices corresponding to all values that exceed some threshold value. Then, the maximum and minimum indices found will be the start and end points you are looking for - so you can then use
y_new = y( min( f ) : max( f ) )
and similar if you have a time array also.
You could also expand that out a little bit if you wanted to plot from just outside this range to see it take it's upturn by using something like
y_new = y( min( f ) - n : max( f ) + n )
where n is a number of time-steps by which the range will be expanded in each direction.