Autoregressive (AR) models constants - Time Series Analysis
You have a slight typo in the notation of a AR(1) model. The correct signature is,

$y_t = \beta_0 + \beta_1 \times y_{t-1}+\epsilon_t$ or $y(t) = \beta_0 + \beta_1 \times y(t-1) + \epsilon(t)$,

where $y(t)$ and $\epsilon(t)$ are  random variables. If $y(t)$ is standard Gaussian you can estimate $\beta_{0,1}$ with a maximum likelihood estimator (MLE). If not you will need a more complex method. You can read more about it in this article on estimating at ARMA Process.