  The paper examines the problem of representing the dynamics of low order
autoregressive (AR) models with time varying (TV) coefficients. The existing
literature computes the forecasts of the series from a recursion relation.
Instead, we provide the linearly independent solutions to TV-AR models. Our
solution formulas enable us to derive the fundamental properties of these
processes, and obtain explicit expressions for the optimal predictors. We
illustrate our methodology and results with a few classic examples amenable to
time varying treatment, e.g, periodic, cyclical, and AR models subject to
multiple structural breaks.
