I am really trying, but struggling, to understand how Autoregressive and Moving Average work. I am pretty terrible with algebra and looking at it doesn't really improve my understanding of something. What I would really love is an extremely simple example of say 10 time dependent observations so I can 'see' how they work. So let's say you have the following data points of the price of gold:
Time Gold Price ($) 1 4 2 6 3 6 4 8 5 7 6 6 7 4 8 3 9 3 10 4
For example, at time period 10, what would the Moving Average of Lag 2, MA(2), be? Or MA(1)? And AR(1) or AR(2)?
I traditionally learned about Moving Average being something like:
(sum of n observations)/n
But when looking at ARMA models, MA is explained as a function of previous error terms, which I can't get my head around. Is it just a fancier way of calculating the same thing?
I found this post helpful: (How to understand SARIMAX intuitively?) but whist the algebra helps, I can't see something really clearly until I see a simplified example of it.