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Canonical correlation analysis of stochastic trends via functional approximation

Massimo Franchi, Iliyan Georgiev, Paolo Paruolo

arXiv 29 Nov 2024 · Econometrics · publishedJournal of the American Statistical Association (2026)

arXiv:2411.19572 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper proposes a novel approach for semiparametric inference on the number $s$ of common trends and their loading matrix $\psi$ in $I(1)/I(0)$ systems. It combines functional approximation of limits of random walks and canonical correlations analysis, performed between the $p$ observed time series of length $T$ and the first $K$ discretized elements of an $L^2$ basis. Tests and selection criteria on $s$, and estimators and tests on $\psi$ are proposed; their properties are discussed as $T$ and $K$ diverge sequentially for fixed $p$ and $s$. It is found that tests on $s$ are asymptotically pivotal, selection criteria of $s$ are consistent, estimators of $\psi$ are $T$-consistent, mixed-Gaussian and efficient, so that Wald tests on $\psi$ are asymptotically Normal or $\chi^2$. The paper also discusses asymptotically pivotal misspecification tests for checking model assumptions. The approach can be coherently applied to subsets or aggregations of variables in a given panel. Monte Carlo simulations show that these tools have reasonable performance for $T\geq 10 p$ and $p\leq 300$. An empirical analysis of 20 exchange rates illustrates the methods.

Citation extraction

49
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Phillips, P. C. B (2014) Optimal estimation of cointegrated systems with irrelevant instruments0.94112483%
2Onatski, A. and C. Wang (2018) Alternative Asymptotics for Cointegration Tests in Large VARs0.8749467%
3Bierens, H (1997) Nonparametric cointegration analysis0.87452100%
4Johansen, S (1996) Likelihood-based Inference in Cointegrated Vector Auto-Regressive Models0.83922859%
Johansenunmatched citation key Johansen0.8307286%
6Johansen, S (1991) Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models0.81142100%
7Phillips, P. C. B (2005) HAC Estimation by Automated Regression0.81142100%
Phillipsunmatched citation key Phillips0.7374275%
9Ahn, S. and A. Horenstein (2013) Eigenvalue Ratio Test for the Number of Factors0.73732100%
10Bykhovskaya, A. and V. Gorin (2022) Cointegration in large VARs0.73732100%

Showing the top 10 of 96 scored citations. 2 of these could not be matched to a bibliography entry, so only the citation key is shown.