Inference on the attractor spaces via functional approximation

This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations and functional approximation of Brownian motions, and it can be applied both to the whole system and or to any set of linear combinations of it. The hypotheses of interest are cast in terms of the number of stochastic trends in specified subsystems, and inference is based either on selection criteria or on sequences of tests. This paper derives the limit distribution of these tests in the special one-dimensional case, and discusses asymptotic properties of the derived inference criteria for hypotheses on the attractor space for sequentially diverging sample size and number of basis elements in the functional approximation. Finite sample properties are analyzed via a Monte Carlo study and an empirical illustration on exchange rates is provided.

💡 Research Summary

This paper develops a semiparametric inference framework for testing inclusion restrictions on the attractor space (the space spanned by common stochastic trends) of I(1) multivariate time‑series when the cross‑sectional dimension p is moderate but fixed and the time dimension T and the number of basis functions K used in a functional approximation both diverge. The authors build on empirical canonical correlations between the observed p‑dimensional series Xₜ and a K‑dimensional vector of deterministic functions dₜ that form the first K elements of an orthonormal L²