[Math] How to find autoregressive coefficients of ARMA model

Question

I am searching various sources to find the method of manually calculating coefficients of Auto Regressive Moving Average model. The following is the text I found in a book. My question is how a₁ and a₂ are found. Can any one please help.

"Higher-order autoregressive models include more lagged y_t terms as predictors. For example, the second-order autoregressive model, AR(2), is given by
$$
y_{t}+a_{1}y_{t-1}+a_{2}y_{t-2}=e_{t}
$$
where a₁ , a₂ are the autoregressive coefficients on lags 1 and 2."

Answer 1

Using maximum likelihood method.