Asymptotic inference for monstationary fractionally integrated processes

This paper studies the asymptotic of nonstationary fractionally integrated (NFI) multivariate processes with memory parameter d> 112. We provide conditions to establish a functional central limit theorem and weak convergence of stochastic integrals for NFI processes under the assumptions of these results are given. More specifically, we obtain the rates of convergence and limiting distributions of the OLS estimators of cointegrating vectors in triangular representations. Further, we extend Sims, Stock and Watson's (1990) analysis on estimation and hypothesis testing in vector autoregressions with integrated processes and deterministic components to the more general fractional framework. We show how their main conclusions remain valid when dealing with NFI processes. That is, whenever a block of coefficients can be written as coefficients on zero mean 1(0) regressors in a model that includes a constant term, they will have a joint asymptotic normal distribution, so that the corresponding restrictions can be tested using standard asymptotic chi-square distribution theory. Otherwise, in general, the associated statistics will have nonstandard limiting distributions.