Time Series Analysis with Gaps in Data - is it possible?

Hey everyone,

I am currently doing a coursework for uni and I need some help. I don't have a background in stats and this is not a statistics course so I am confused.

I have a dataset of daily air quality, which have numerous gaps - some small (one day missing), some big (over a month of data).
I want to calculate the running mean, residual and autocorrelation of the data but is this possible with so many gaps? Ive looked for quite a bit but cant find data without gaps (and i dont have time to look much further because deadline is quite soon, which is my fault lol).

thank you so much in advance.

p.s. if anyone happens to have similar data that doesnt have gaps, please let me know!
A quick google gave this. https://aqicn.org/data-platform/register/ Any use?
I tried my city and it had a very occasional gap which you can fill in with the average from the days before and after.
There must be other sites, I imagine.
Oh wow this is so cool! How neat! Thank you so much katxt.
Just browsed and yeah the gaps seems to be much smaller and more manageable.
I dont know where i went wrong with my data search but this is so handy so thanks again.