To answer Ridley's questions:
Easiest to answer with an example:
7 Day trailing average for 6 September is an average of 31 August to 6 September.
5 Day centred average for 6 September is an average of 4 September to 8 September
So, the trailing average lags because it only considers what has happened, it has the advantage that you have today's trailing average today. The centred average is in some ways more accurate as it averages days on both sides of the day in question, but, you have to wait a couple of days to get the number.
The days chosen and lengths have little logic! I started by doing a 7 day trailing average because it is a week and I get the number on the day. I added the 5 day average as a contrast and also made it centred to give more contrast. So, no real logic to these decisions. The good thing about 2 averages, differently calculated, is that you get 2 views of the situation: the 5 day centred average may be a couple of days behind but it responds much quicker to changes, so a quicker, but more volatile, view of the trend. The 7 day average is slower to react but a more reasonable period of time. A 14 day average, given the period people are infectious, is actually a good measure for this virus.
As with any stats you can make the numbers sing to your own tune, at least to some extent. If I wanted our numbers to look good I could plot them, per 1million persons, against those in the USA. If I want Australia to look bad, do the same in comparison to New Zealand. Can also cherry pick data. I started from the start of July because that is when the second wave in Victoria seemed to take off, and being the start of the month is convenient for organising how we see things.
The first time I used the centred average I just called it the 5 day average, for the simple reason that, for the life of me, the word centred wouldn't come into my brain!
DS