Try this and tell me if it is what you wanted:
dayFilter=and(hour(Date)>=6,hour(Date)<=18); %creates a filter for day hours
nightFilter=~and(hour(Date)>=6,hour(Date)<=18);
day=Date(dayFilter); %applies filter
Absolute_VTEC_day=Absolute_VTEC(dayFilter); %restrict the x axis, the number of elements need to match otherwise you cannot plot
night=Date(nightFilter);
Absolute_VTEC_night=Absolute_VTEC(nightFilter);
figure
plot (day,Absolute_VTEC_day) %plots
figure
plot (night,Absolute_VTEC_night)
The comments are for the day section, but they are still valid for the night. Conceptually they are the same.
Left is the night. right is the day. You nned to format the figures as you prefer. 
