How do you model time series data with an autogressive model?

Question

$(1.)$ Given an $n$-value time series $\{c_1, \dots, c_{n}\}$, how would you model this with an autoregressive model of order $M$?

$(2.)$ Assuming an AR process of order $M = 2$, how would you estimate $a_0, a_1, a_2$ and $\sigma_v^2$? Where $\sigma_v^2 = \text{Variance}(v(n))$ and $v(n)$ is a white noise random process.

I understand that a time series $\{x(n)\}$ is generated by an autoregressive model iff $\sum_{k=0}^M a_kx(n-k) = v(n)$ where $v(n)$ is a white noise variable.

But how would I model a time series with an autoregressive model of order $M$? I don't have any idea how to even start this. How would I put this data into an autogressive model?

Answer 1

Simply create two lags ( predictor series) of your series and estimate a regression equation with an intercept. This will give you the three a's and the error variance