Time-varying vector error-correction models: estimation and inference

This paper considers a time-varying vector error-correction model that allows for different time series behaviors (e.g., unit-root and locally stationary processes) to interact with each other and co-exist. From a practical perspective, this framework can be used to estimate shifts in the predictability of non-stationary variables, and test whether economic theories hold periodically, etc. We first develop a time-varying Granger Representation Theorem, which facilitates the establishment of an asymptotic theory for the model, and then propose estimation and inferential methods for both short-run and long-run coefficients. We also propose an information criterion to estimate the lag length, a singular-value ratio test to determine the cointegration rank, and a hypothesis test to examine the parameter stability. Finally, we extend the framework to allow for unknown structural breaks in either cointegration relationship or time-varying coefficient functions. To validate the theoretical findings, we conduct extensive simulations, and demonstrate the empirical relevance by testing the present value model for stock returns.