AR Models

AR(1): use $x_{t-1}$ to express $x_t$. AR(p): use $x_t-1, x_t-2, ..., x_t-p$ to express $x_t$.

If these 3 conditions are not satisfied, our estimation results will not have real-world meaning. Our estimates for the parameters will be biased, making any tests that we try to form using the model invalid. Unfortunately, it can be a real pain to find a covariance-stationary time series in the wild in financial markets.

There are ways, however to make a non-stationary time series stationary. Once we have performed this transformation, we can build an autoregressive models under the above assumptions.