Abstract

This paper proposes a novel approach for semiparametric inference on the number s of common trends and their loading matrix ψ in I(1)/I(0) systems via functional approximation, based on empirical canonical correlations between p observed time series of length T and the first K discretized deterministic elements of an L² basis. It proposes tests and selection criteria on s and estimators and tests on ψ, and it discusses their properties as T and K diverge sequentially for fixed p and s. The approach can be applied coherently to panels of p variables with a generic number s of stochastic trends, as well as to subsets or aggregations of variables. It is found that tests on s are asymptotically pivotal, selection criteria of s are consistent, estimators of Ψ are T-consistent, mixed-Gaussian and efficient, so that Wald tests on Ψ are asymptotically Normal or χ². The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. Monte Carlo simulations show that these tools have reasonable performance for T ≥ 10 p and 0 < p ≤ 300. An empirical analysis of 20 exchange rates illustrates the methods.