Rissanen's Theorem and Econometric Time Series

In a typical empirical modeling context, the data generating process (DGP) of a time series is assumed to be known up to a finite-dimensional parameter. In such cases, Rissanen’s (1986) theorem provides a lower bound for the empirically achievable distance between all possible data-based models and the true DGP. This distance depends only on the dimension of the parameter space. The present paper examines the empirical relevance of this notion to econometric time series and discusses a new version of the theorem that allows for nonstationary DGP’s. Nonstationarity is relevant in many economic applications and it is shown that the form of nonstationarity affects, and indeed increases, the empirically achievable distance to the true DGP.