Physically understanding autoregressive model (really basic question) I would like to basically understand what an autoregressive model is used for (so I don't really attempt maths in the answers).

I just started a signal processing course and the model was introduced.

This is what I understood but I don't think I understood it well :

We have $n-1$ samples of a signal and we want to guess what the $n$'th will be.

With Young Walker, we have an approximation of the $n$'th sample that is : $\tilde{x}[n]=\sum a_k x[n-k]$

But $\tilde{x}[n]$ is just an approximation of $x[n]$.

So we have : $x[n]=\tilde{x}[n]+\epsilon$ where $\epsilon$ is the "error" I make when I use $\tilde{x}[n]$.

The autoregressive models assumes that $\epsilon$ is a white noise with average zero (and this makes sense because there is no reason in our model to have more often $\tilde{x}[n]&gt;x[n]$ than $\tilde{x}[n]&lt;x[n]$ ).

Did I understand the physical meaning of the model well ?

Thanks !!
Your understanding is right. Just a few points...


I think you meant Yule-Walker equations.
It is better to distinguish $N$ from $n$. In an AR($N$) model we consider last $N$ terms to approximate the next term. 
An important interpretation that you missed was the fact that when we consider
$$\epsilon=x[n]-\tilde{x}[n]=x[n]-\sum_ka_kx[n-k],$$ or in a more standard way (representing the process by variable $y$ instead of $x$
$$y[n]=\sum_ka_ky[n-k]+\epsilon[n],$$
it can be seen as an input-output relationship of an LTI filter, $\epsilon[n]$ being input and $y[n]$ the output. More specifically, 



   AR model can be seen as the output of an all-pole IIR filter which is excited by a white noise input.