The Fundamental Properties of Time Varying AR Models with Non Stochastic Coefficients
31 Pages Posted: 21 Mar 2014
Date Written: March 15, 2014
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.
Keywords: abrupt breaks, covariance structure, cyclical processes, homogeneous and particular solutions, optimal predictors, periodic AR models
JEL Classification: C22, C53, C58
Suggested Citation: Suggested Citation