The fundamental properties of time varying AR models with non stochastic coefficients

Abstract

The paper examines the problem of representing the dynamics of low order autoregressive models with variable coefficients. The existing literature computes the forecasts of the series from a recursion relation. Instead, we provide their linearly independent solutions. 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 models subject to multiple structural breaks.