Inference on the attractor spaces via functional approximation

TL;DR

This paper develops semiparametric inference methods for hypotheses on cointegration and attractor spaces in high-dimensional $I(1)$ processes, using empirical canonical correlations and functional approximation of Brownian motions.

Contribution

It introduces a novel approach combining empirical canonical correlations with functional approximation for inference on attractor spaces in large-dimensional systems.

Findings

Derived limit distribution for one-dimensional case tests.

Analyzed asymptotic properties of inference criteria.

Validated finite sample performance through Monte Carlo and empirical exchange rate data.

Abstract

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.