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.
Ploberger, Werner and Phillips, Peter C.B., "Rissanen's Theorem and Econometric Time Series" (1998). Cowles Foundation Discussion Papers. 1445.