An Autoregressive process of order 1 (AR(1)) is expressed as:
$$ y_{t} = \phi \, y_{t-1} + \epsilon_{t}, \quad |\phi| < 1, $$
where \(\epsilon_{t}\) is white noise (typically with distribution \(N(0, \sigma^2)\)). This process is stationary when \(|\phi| < 1\), and therefore, the Ordinary Least Squares (OLS) estimation of the parameter \(\phi\) tends to follow a normal distribution as the number of observations increases.
On the other hand, when \(\phi = 1\), the process ceases to be stationary and becomes a Random Walk:
$$ y_{t} = y_{t-1} + \epsilon_{t}, $$
whose differenced form is:
$$ \Delta y_{t} = y_{t} - y_{t-1} = \epsilon_{t}. $$
In this case, the estimation of \(\phi\) (when estimated as if it were an AR(1)) does not follow the conventional asymptotic normal distribution and tends to be biased towards values greater than 1, highlighting the non-stationary nature of the process.