Try to adapt this to your code.
l = ([u'VESSELTYPE', u'VESSELNAME', u'PERIODSTART', u'PERIODEND', u'ESTREDELI', u'HIRE', u'DAYS Mar-14', u'DAYS Q2 2014', u'DAYS Q3 2014', u'DAYS Q4 2014', u'DAYS Q1 2015', u'DAYS Q2 2015', u'DAYS Q3 2015', u'DAYS Q4 2015', u'NUMDAYS'], 'AnotherItem')
days = [s for s in l[0] if s.startswith('DAYS')]
print days
You can use the "startswith()" method available to all strings and make some logic with it.
If you don't like list-comprehensions, here's its equivalent in a for-loop:
days = []
for s in l[0]:
if s.startswith('DAYS'):
days.append(s)
print days